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Digital Image Acquisition and Processing inMedical X-Ray Imaging

Til Aach and Ulrich Schiebel and Gerhard Spekowius

in: Journal of Electronic Imaging. See also BIBTEX entry below.

BIBTEX:@article{AAC99a,author = {Til Aach and Ulrich Schiebel and Gerhard Spekowius},title = {Digital Image Acquisition and Processing in Medical

X-Ray Imaging},journal = {Journal of Electronic Imaging},

publisher = {SPIE},volume = {8},number = {Special Section on Biomedical Image Representation},year = {1999},pages = {7--22}}

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A reprint from

Electronic IrnagingtssN l0l7-9909

January 1999

Digital image acquisition and processing in medical x-ray imaging

Til AachUlrich Schiebel

Gerhard Spekowius

Journal of Electronic lmaging 8(1), 7-22 (January 1999).

Digital image acquisition and processing inmedical x-ray imaging*

Til AachTLIlrich Schiebel

Gerhard SpekowiusPhilips GmbH Research Laboratories

Weisshausstrasse 2D-52O66 Aachen, Germany

E-mail: aach @informatik.mu-luebeck.de

Abstract. This contribution discusses a selection of today's tech-niques and futurc concepts for digital x-ray imaging in medicine.Advantages of digital imaging over conventional analog methodsinclude the possibility to archive and transmit images in digital intor-mation systems as well as to digitally process pictures before dis-play, for example, to enhance low contrast details. After reviewingtwo digital x-ray radiography systems for the capture of süll x-rayimages, we examine the real time acquisition of dynamic x-ray im-ages (x-ray fluoroscopy). Here, particular attention is paid to theimplications of introducing charge-coupled device cameras. Wethen present a new unified radiography/fluoroscopy solid-state de-tector concept. As digital image quality is predominantly determinedby the relation of signal and noise, aspects of signal transfer, noise,and noise-related quality measures like detective quantum effi-ciency feature prominently in our discussions. Finally, we descibe adigital image processing algorithm for the reduction of noise in im-ages acquired with low x-ray dose. @ 19ss SptE and tS&T.[s1 01 7-e909(99)00401 -8]

1 lntroduction and Overview

In this paper, we discuss selected current topics of digitalimage acquisition and processing in medicine, focusing onx-ray projection imaging. A key feature of digital imagingis the inherent separation of image acquisition and display.Whereas analog screen/film combinations (Fig. 1) use filmas a medium for both image recording and viewing, digi-tally acquired images can be processed in order to correctaccidental over- or underexposure, or to enhance diagnos-tically relevant information before display. Also, digital im-ages can be stored and fransmitted via picture archiving andcommunication systems (PACS),' and be presented on dif-ferent output devices, like film printers or cathode ray tube(CRT) monitors (softcopy view in g).

*Partly presented m m inyited paper at th€ Intemational Symposium on ElecuonicPhotography (ISEP: a PHOTOKINA event), Cologne, Gemmy, Sept. 21-22,1996.

iT. Aacb is now witb rhe Medical University of Luebeck, hstitute for Sipal Pro-cesshg md hmess Control, Rataburger Allee 160, D-23538 Luebeck, Gemmy.

Paper 97010 reeived Apr. 1, 1997; revised mmuscript rrceived May i, 1998; ac-cepred for publication June 1, 1998.1017-9909/99/510.00 O 1999 SPIE and IS&T.

The separation of image acquisition and display in adigital system is illustrated by comparing analog and digitalacquisition of silgle high resolution projection images (x-ray radiograpäy). The principle of the imaging serup issketched in Fig. 2. X radiation passes through the patientbefore exposing a detector. Widely used for image detec-tion are analog screen/film combinations as shown in Fig.1, which consist of a fiIm sheet sandwiched between thinphosphor intensifying screens. The phosphor screens con-vert the incoming x radiation into visible light blackeningthe film, which, after developing, is examined by viewingon a lightbox.

Well-established digital alternatives include storagephosphor systems (SPS),'* also known as computed radi-ography (CR) systems, and a selenium-detector based digi-tal chest radiography system [(DCS),

"Thoravision"].''o InCR systems, the image receptor is a photostimulable phos-phor plate, which absorbs and stores a significant portion ofthe incoming x-ray energy by trapping electrons and holesin elevated energy states. The stored energy pattern can beread out by scanning the plate with a laser beam. The emit-ted luminescence is detected by a photomultiplier and sub-sequently digitized. Common plate sizes are 35X35 cm2sampled by a 1760X 1760 matrix, 24x30 cm2 sampled bya 7576X1976 matrix, and for high resolutions 18x24 cmz sampled by a 1770x2370 matrix. The resultingNyquist frequencies are between 2.5 and 5 lp/mm. An ex-ample CR image is given in Fig. 3.

The detector of a DCS consists of an amorphous sele-nium layer evaporated onto a cylindrical aluminum drum.Exposure of the drum to x radiation generates an electro-static charge image, which is read out by electrometer sen-sors. Maximum size of the sampled image matrix is 2166x2448 pixels, with a Nyquist frequency of 2.7 lp/mm.

In analog as well as in digital systems, the acquired ra-diographs are degraded by nonideal system properties.These include limitations of contrast and resolution, and aredescribed for instance by the modulation transfer function(MTF). Other undesired effects are spatially varying detec-tor sensitivity and unwanted offsets. Additional degrada-tions can be introduced by accidental over- or underexpo-

Journal of Electronic Imaging / January 1999 / Vol. B(1) / 7

Aach, Schiebel, and Spekowius

x-roy film

iT,::'ÄY.nFig, 1 Principle of conventional x-ray image detection by a screen/film combination. The lighfsensitive film is sandwiched between twophosphor intensifying screens which convert the incoming x radia-tion into visible l ight.

sure. Unlike screen/film systems, however, digital systemsenable the compensation of such known degradations bysuitable processing like gain and offset correction and MTFrestoration. Furthermore, the problem of over- or underex-posures is virtually eliminated by the wide latitude of theSPS and DCS image receptors (about four orders of mag-nitude) and the possibility to digitally adjust the displayedintensity range. Finally, methods like "unsharp masking"and "harmonization" can be employed to enhance relevantdetail with respect to diagnos,tically less important informa-tion, and to optimize image presentation on the selectedoutput device.'-'" Figure 4 shows the result of applyingsuch enhancement techniques to the radiograph in Fig. 3.

As we will see, the predominant factor limiting the ex-tent up to which MTF restoration and optimization of im-age presentation can be successful is the noise level presentin a digital image. Rather than by traditional quality mea-sures like MTF or radiographic speed of screen/film com-binations, the imaging performance of electronic systems istherefore described by measures capturing the signal-to-noise transfer properties, like signal-to-noise ratio (SNR),noise equivalent guanta (NEO and detective quantum effi-ciency (DQE).r'o'r' An imaging-inherent noise source is thediscrete nature of x radiation, generating so-called x-rayquantum noise in the acquired images. This fype of noise isparticularly relevant for images recorded with very lowx-radiation doses, and affects both analog and digital imag-ing systems. Clearly, noise introduced within the imagingsystem during later processing stages, e.g., quantizationnoise during analog-to-digital (A/D) conversion, can fur-ther deteriorate the imaging performance. Noise behaviortherefore features prominently in our discussions.

In the next section we review x-ray image qualiry mea-sures needed later in the paper. We then consider digitalreal time dynamic x-ray imaging, known as x-ray fluoros-copy. Here, we pay particular attention to differences in

,

Fig. 2 Principle of x-ray projection radiography (view from above, 1:x-ray tube, 2'. xray beam, 3: patient, 4: detector).

8 / Joumal of Electronic lmaging / January 1999 / Vol. 8(1)

Fig. 3 Portion of size 700x 1846 pixels from a radiograph of a foot(dorso-plantar) acquired by a CR system.

noise behavior of electronic camera tubes (Sec. 3.3) andsolid-state charge-coupled device (CCD) cameras (Sec.3.4). This is followed by a discussion of a new flat solid-state x-ray sensor for both digital x-ray fluoroscopy andhigh resolution radiography. Finally, in Sec. 5, we describea recently developed quantum noise reduction filter.

2 X-Ray lmage Detection

An x-ray tube generates x radiation by accelerating elec-fions i,n an electric field towards a tungsten anode. On hit-ting the anode, about lVo of the electrons generate x-rayquanta, which leave the tube through an x-ray transparentwindow. The x-ray beam consists of a discrete number ofx-ray quanta of varyilg energy, with the maximum energybeing limited by the applied tube voltage. Typical valuesfor the tube voltage range between 60 and 150 kV. Theenergy distribution of the x-ray quanta determiaes the beamqwlity. A thin aluminum plate about 3 mm thick, whichabsorbs low-energy x-ray quanta unable to pass through thepatient, is integrated directly into ttre tube window. These

Digital x-ray imaging

quanta would only add to the absorbed patient dose withoutcontributing to the imaging process. In the following, thethus reduced range of energies is approximated by a single,average energy, i.e., we assume monoenergetic x radiation.For tube voltages of 150 and 60 kV, these average energiesare about 63 and 38 keV, respectively.

Owing to the discrete nafure of x radiation only a lim-ited, potentially small number of x-ray quanta contributesto the imaging process at each pixel. For instance, in x-rayfluoroscopy the typical x-ray dose for an image is about 10nGy at a beam quality of 60 keV. This results in a quantumflow q6 of roughly qs:300 quanta.imm2. X-ray quanrumnoise is caused by random fluctuations of the quantumflow, which obey a Poisson distribution.l2 Therefbre, thestandard deviation o of quantum noise is proportional toJqo. er the detected signal S is proportional to qs, the

Fig, 5 Schematic diagram of an efficiency stage of an x-ray detec-tor, which absorbs only a fraction a ol the incoming quantum flowQ o '

SNR S/o varies with 1,Q0, u"d decreases with decreasingx-ray dose.

A real detector absorbs only a fraction of the incomingx-ray quanta given by the detector absorption fficiency a(Fig. 5). The squared signal-to-noise ratio at the output ofthis fficiency stage obeys

^ 51... o2a7SNR1,,,:-#

Ü1u, aQo

and is equal to the effective number of absorbed x-rayquanta. The squared SNR is therefore also referred to asnoise equivalent quantd (NEQ). Normalizing SNRI,, by 4syields the so-called detective quantum fficiency (DQE).For the efficiency stage in Fig. 5, the DQE is identical tothe absorption efficiency a. As q6 corresponds to thesquared input SNR, the DQE can also be interpreted as theratio SNRl,r/SNR'�,,.

The so far simplified treatrnent of NEQ and DQE con-sidered only homogeneous exposures with a spatially con-stant quantum flow 4s, and neglected noise generated bythe detector system. In the following, we present more gen-eral definitions of spatial frequency-dependent NEQ andDQE for electronic imaging systems, including effects of anonideal detector MTF and detector noise. The originaldefinitions of NEQ and DQE for photograp,hic systems canbe found in Refs. 13 and 14 (cf. also Ref. 11).

Figure 6 shows the diagram of our detector model. Theefficiency stage is followed by a gain factor G, which de-scribes the conversion of x-rgy quanta into other informa-tion carriers, e.g., electrons for the solid-state detector dis-cussed in Sec. 4. This is followed by a stage of spatiallyscatterixg the information carriers, which results in a spatiaiblur. This is described by a linear modulation transfer func-tion (MTF) I/(a), which decreases over the spatial fre-quency u. Finally, system noise with power spectrumNlr,(u) is added. The power specrrum Nl of the incomingquantum noise is flat,r) and its power spectral density isshown in Appendix A to be equal to the quantum flow 40.

Clearly, at zero spatial frequency, i.e., for a homoge-neous exposure with quantum flow qo, the output signal isgiven by

e? dct --{tH Htu) l--$y-:et

Ni' ------r Y r '-'r Y N'."

C N ; "

Fig, 6 Schematic of an x-ray detector comprising an etficiencystage fol lowed by a conversion with gain G, a l inear MTF H(u), andaddit ive system noise with NPS N!"".

Fig. 4 Enhanced version of Fig. 3. First, middle and high spatialfrequencies were amplified relative to very low ones in order tomake such details better visible (harmonization). In a second stage,the image was given a sharper appearance by additional amplifica-tion of high spatial frequenciesby unsharp masking.

Journal of Electronic lmaging/January 1999/Vol. B(l)/9


S, , , ( 0 ) : 4odG,

since 11(0): 1. Noise at the detector output consists of theoriginally white quanfum noise filtered by the system trans-fer function and of system noise. Its power spectrumtt!,,1u1 is

N7, ,@):qoaczH2(u)+l r ] r , (a) . (3)

We now consider an almost homogeneous exposure with asinusoidally varying quantum flow q(u,x):eoll* e stn(2mrx)], where x is a spatial coordinate, and 0<e( l. This exposure is recorded with the s€rme x-ray dose asthe previous homogeneous exposure, since the spatially av-eraged quantum count {(u) is identical to 4s. The outputamplitude S our(u) of the sinusoid component is given by

S ou , (u ) : q6eaGH(u ) . ( 4 )

The noise equivalent quanta NEQ,,,(u) as a function ofspatial frequency is now defined as

Fig. 7 Sketch of a tluoroscopy system [1 : movable C arm, 2: x-raytube, 3: x-ray beam, 4: patient, 5: operating table, 6: detection frontend, 7: video signal ied to processing unit and monitor (not shown)1.

Hence, the larger the actually encountered output noise inrelation to the fiItered quantum noise, the lower the DQE is.

From Eq. (7), a measure can be derived which indicateshow far linear signal restoration is possible without dispro-portionate noise amplification. Requiring the NPS after res-toration to be flat, the following restoration filter I/a(a) caneasily be derived:

boE(r)Hn(u): VDö u- ' ( , ) . (8)

Evidently, low values for DQE(z)----caused by-increasednoise leveis-allow only a correspondingly lower restora-tion to be applied. For a noiseless ideal system, the DQE inEq. (8) is frequency independent and permits full restora-tion by inverse filtering.

3 Digital X-Ray FluoroscopyX-ray fluoroscopy is a real time dynamic x-ray imagingmodality which allows a physician to monitor on-line clini-cal procedures like catheterization or injection of contrastagents. An x-ray fluoroscopy system is sketched in Fig. 7: amovable C-shaped arm bearing the x-ray tube and the im-age detection "front end" is mounted close to the operat-ing table. The position of the C arm can be adjusted arbi-trarily during the clinical procedure. The detected dynamicimages are displayed on a CRT monitor placed near theoperating table, hence providing the physician with imme-diate visual feedback.

3.1 Fluoroscopy lmage Detection

Today's detection front ends consist of an x-ray image in-tensifier. - (XRII) coupled by a tandem lens to a TVcamera,'o't' which is followed by an A./D converter (Fig.8). The XRII is a vacuum tube containing an enüancescreen attached directly to a photocathode, an electron op-tics, and a phosphor screen output window. Images are de-tected by a fluorescent caesium iodide (CsI) layer on theentrance screen, which converts the incoming x-ray quanta

/ . ) \

svn],,,(u.1NEQ,,,( u)= qo *ffi:

qlozczn2lu)qsacz H21u) + N :y ,@) '

To interpret this quantify, we consider the case of vanishingsystem noise, that is, lflr"(r):0 for all u. Both signal andnoise are then filtered by the same transfer function I1(u),resulting in NEQ,ur(a): aqo, which does not depend on nanymore. Assuming that the MTF II(a) is different fromzero for all a, the original signal can be restored by inversefiltering with t1-1(u). Simuhrneously, this operation trans-forms the lowpass-shaped noise power spectrum (NPS)N'"*(u) again into a flat NPS.

Nonvanishing system noise decreases the NEQ, espe-cially at those spatial frequencies where Nlrr(a) exceedsthe filtered quantum noise spectrum. As in practice systemnoise is often white, this is generally the case for higherspatial frequencies, where the filtered quantum noise spec-trum is small. Restoration by inverse filtering would nowresult in unacceptably boosted system noise.

As before, the detective quantum efficiency is defined asnoise equivalent quanta normalized by the spatially aver-aged incoming quantum flow qs:

NEQ,, , (u) SNR3,, (a)DQE(a )

Qo SNRi(u)

qrazGzH2lul

qoaczH2(u)+N3),(u)(6)

Example DQE curves for a real system are given below(Fig. 16). Denoting the output NPS in the ideal case ofvanishing system noise by Nio@), the DQE can be rewrit-ten as

t t?,( u)DQE('I) : ";#. \7)

tY out\u J

1 0 / Journal of Electronic I maging / January 1 999 / Vol. 8(1 )

(s)


Fig, I Detector tront end of a fluoroscopy system (1 : XRll tube, 2:input screen and photocathode, 3: electron optics, 4: output window,5: tandem lens, 6: TV camera, 7: amplif ier).

into visible photons, which in turn reach the photocathode.The CsI screen is a layer approximately 400 ;r.m thick andevaporated onto an aluminum substrate. The absorption ofthese screens is about 607o-707o.16'18 In addition, ai shownin Fig. 9, CsI is grown in a needle-like structure such thatthe individual needles act as optical guides for the gener-ated light photons. This prevents undesired lateral propaga-tion within the CsI layer, and thus ensures a relatively goodscreen MTF (see Fig. 13).

The generated photoelectrons are accelerated when pass-ing through the electron optics and focused onto the outputwindow, where they generate luminescence photons. Theresulting visible pictures are then picked up by the camera.The diameter of the circular XRII entrance screen rangesbetween 15 and 40 cm, depending on the application, whilethe diameter of the XRII output window is between 25 and50 mm. Apart from image intensification, the electron op-tics allow demagnification, and zooming by projecting asmall subfield of the entrance screen onto the output win-dow.

To pick up the images from the XRII output window,electronic camera tubes Iike plumbicons, vidicons or sati-cons are still in wide use today. In Europe, camera readoutis mostly with 625 lines/image, with the full frame rate of25 images per second in interlaced or progressive format.However, special high resolution modes (1250 lines/image)are also often available. In applications where temporalresolution is less critical, the frame rate can be reduceddown to only a single image per second (Iow frame ratepulsed fluoroscopy) in order to save x-ray dose. The analog

Fig, 9 Electron-microscopic image of the cross section of a Csllaver.

Fig. 10 Sample image f rom a fluoroscopy sequence, partly showinga patient's spine and a guidewire. The circular image boundary iscaused by the cylindrical shape of the XRll.

video signal is then amplified and fed to an 8 bit-10 bitA./D converter. In case of digitization by 8 bit, the gain ofthe amplifier is higher for smaller signal amplirudes thanfor larger ones in order to enhance dark parts ofthe images.This is commonly referred to as analog white compression.An example of a fluoroscopy image is depicted in Fig. 10.

3.2 Main Noise Sources in Fluoroscopy lmageDetection

The SNR attainable in fluoroscopy is inherently limited bythe low x-ray quantum flow 4s, which, as discussed in Sec.2, generates relatively strong quantum noise in relation tosignal.

System-internal noise sources include so-called fixedpattenx noise, arrd signal shot noise. Fixed pattern noise ismainly caused by inhomogeneities of the XRII outputscreen, which are stable over time. Signal shot noise isgenerated by the discrete nature of the conversion of infor-mation carriers, e.g., from luminescence photons into elec-trons in the XRII photocathode and the camera. As thepower spectrum of signal shot noise is approximately flat,while the spectrum of quantum noise is lowpass shaped,shot noise can affect the SNR and the DQE mostly for highspatial frequencies. Still, signal shot noise is often negli-gible compared to x-ray quantum noise.

3.3 Noise in Camera Tubes

The visible images are projected from the XRII output win-dow onto the photoconductive target layer of the camerarube, which for plumbicons, consists of lead oxide (PbO).The resulting electrostatic charge image is then read out byscanning the target layer linewise with an electron beam(scanned device). Line-by-line scanning means that sam-pling in the vertical direction is carried out directly on thephotoconductive target, with the size of the electron beamspot being sufficiently large to prevent alias. Horizontalsampling is done later at the A,/D converter.

Journal of Electronic lmaging / January 1999 / Vol. 8(1) / 1 1

\ horiz. NPS -'\\

.,.r\., .\\\\


0.=c

-ci(E

a

z

0 0.5 1 1.5 2 2.5 3spatial frequency flp/mml

Fig. 11 Horizontal cross section of an NPS for an XRll/camera tubesystem before horizontal sampling. The rise of the NPS between 0.5and 1.0 lp/mm is due to the highpass characteristic ot the amplifier,which compensates the lowpass transfer function of the plumbicontarget layer. The NPS drops off again for frequencies larger than 1lp/mm due to bandwidth limitations and the antialias filter.

Unavoidable capacitances of the target layer itself aswell as of the subsequent first amplifier stage act as a low-pass filter, which attenuates high frequency signal compo-nents. This attenuation has to be compensated by ahighpass-like transfer function of the amplifier, which,however, also amplifies high-frequency components oforiginally white ele-ctronic noise. This effect is referred toas triangular noise,t" because bandwidth limitations and anantialias filter before the A,/D converter decrease the noiseamplification again for higher spatial frequencies. Theoverall effect is a triangle-shaped NPS as illustrated in Fig.11, giving this type of noise its name. Due to the linewisescanning, triangular noise increases only with horizontalspatial frequencies, and is independent of vertical spatialfrequencies in the two-dimensional specüal domain.

A typical overall Fourier amplitude spectrum of a homo-geneous x-ray exposure acquired by an XRlVplumbiconchain is shown in Fig. 12, where the gray level representsthe modulus of the Fourier coefficients. The origin (0,0) ofthe spatial frequency axes u,u is in the center of the plot.To avoid an excessive peak at the origin, the average imageintensity was subtracted prior to the Fourier transform.Hence, the shown amplitude specffum corresponds to theobserved realization of noise in the homogeneous exposure.First, a concentration of high Fourier amplitudes can beobserved around the origin, i.e., for low spatial frequencies.This is caused by x-ray quantum noise, and reflects thedrop of the overall system MTF toward higher spatial fre-quencies. Along the horizontal direction, spectral ampli-tudes increase again toward higher spatial frequencies, re-flecting triangular noise. As discussed in the previousparagraph, triangular noise does not occur along the verti-cal spatial frequency axis.

3.4 Noise in CCD-Cameras

Aithough today's XRlVcamera fube combinations achievea good fluoroscopic image quality, it is intended to intro-duce high resolution solid-state CCD sensors into futuresystems in order to further improve image quality. A CCDconsists of a two-dimensional (2D) anay of discrete sensorelements rather than of a "continuous" target plate. Thearray size is usually 5I2x5l2 or I kXl k sensor elements,each of which corresponds to a pixel. The benefits of using

1 2 / Journal of Electronic lmaging / January 1 999 / Vol. 8(1 )

Fig. 12 Two-dimensional Fourier amplitude spectrum of a homoge-neous exposure recorded with an XRll/plumbicon chain. The originof the spatial lrequency axes is in the center of the plot. Thelowpass-shaped quantum noise spectrum, and, in horizontal direc-tion, triangular noise are plainly evident.

a CCD include greater geometrical stability and the absenceof readout jitter. (In an electronic camera tube, readout jit-ter is caused by instability of the electron readout beam.)First, this improves the performance of subtraction fluoros-copy modalities, like digital subtraction angiography,where a background image is subüacted from live imagesto increase detail contrast. Second, the increased geometri-cal stability facilitates the correction of XRtr fixed patternnoise. Note that inhomogeneities of the CCD sensor ele-ments may also require a fixed pattern noise correction.Additionally, CCD cameras exhibit less temporal lag thanpickup tubes. fAmong the mentioned pickup tubes (plum-bicons, vidicons, saticons), plumbicons have lowest lag.]This results in less blurring of moving objects, but ia-creased noise levels due to the reduced temporalintegration.20

The fact that spatial sampling is inherent in a CCD cam-era causes its noise behavior to be fundamentally differentfrom that of pickup tubes. The Nyquist frequency u1s cot-responding to the sampling raster is commonly related tothe XRII entrance plane, and depends on the resolution(512x512 or 1 kX 1 k püels), and the selected XRII zoom.It ranges between 0.7 and 4 lp/mm. Apart from the XRIIand tandem lens, the presampling system MTF is deter-mined by the aperture of each sensor element, which, for anideal sensor, is sinc shaped (Fig. 13). However, as can beseen from the MTF for a CCD-pixel aperture in Fig. 13,integration over the sensor element aperture is generally notsufficient to reduce the MTF for spatial frequencies beyondthe Nyquist frequency to prevent alias. Hence, if the systemMTF is not low (about 57o or less) at uN, noise (and signal)from beyond a1,, is mirrored back to lower spatial frequen-cies, where it increases the observed noise contributions.


totat \ t\ Csl1 k . 1 köhaiä: \ccD

u [p/mm]Fig. 13 Sinc-shaped MTF of the finite aperture of a CCD pixel. Alsoshown are the MTFs of the Csl screen and ot the total imaging chainior a Nyquist frequency of 2.2 lplmm. At this frequency, the pixelMTF is still quite high.

This effect is depicted in Fig. 14. In a pickup rube, suchaliasing is prevented by the size of the electron beam spotand by the antialias filter before sampling the video signal.Triangular noise does not occur in a CCD camera.

A particular alias-based distortion can occur when anantiscatter grid is used in connection with a CCD "ameru.2lAn antiscatter grid consists of thin lead stripes separated byx-ray transparent spacing material, and is mounted close tothe XRtr enüance screen to prevent x-ray quanta scatteredby the patient from reaching the CsI layer. In small XRIImodes, i.e., when zooming to a small subfield of the en-trance screen, the CCD-pixel size-as related to the en-trance plane-approaches the anfiscatter grid spacing. As aresult, Moirt! patterns may occur.

Further CCD-camera noise sources include electron darkcurrent and electronic amplifier noise. The power spectrumof these noise sources is approximately flat up to the Ny-quist frequency.

Similar as in Fig. 12 for pickup tubes, Fig. 15 shows theFourier amplitude spectrum of a homogeneous exposurerecorded by an XRIVCCD chain. The influence of the low-pass shaped quantum noise spectrum is clearly evident, asis the absence of triangular noise. Quantum noise extendsto higher spatial frequencies than in Fig. 12, this is mostlydue to the significantly better MTF of a CCD as comparedto a pickup tube.

=!liased

Fig. 14 NPS al iasing effects induced by sampling in a CCD. Thisfigure depicts the continuous NPS and its shifted version located atthe sampling frequency 2ury. The shaded portion below the Nyquistlrequency u,y adds to the sampled NPS. Also depicted is white sig-nal shot noise.

Fig. 15 Fourier amplitude spectrum of a homogeneous exposurerecorded with an XRll/CCD-camera chain.

Finally, Fig. 16 shows DQE curyes for a 400 pm CsIentrance screen, an entfte 23 cm image intensifier equippedwith such a screen, and a complete imaging chain with a1 kX I k CCD camera. The Nyquist frequency a7y of thissystem is 2.2 lp/mm. Below 2lplmm, the DQEs of both theXRII and the entire chain are almost exclusively deter-mined by the CsI screen. Above 3 lp/mm, the XRII-DQEfalls below the CsI DQE. This is a result of the increasedweight of flat signal shot noise of the photoeiectrons overlowpass-filtered quantum noise and signal for high frequen-cies. The rather steep drop of the DQE for the enrüe imag-ing chain between 2 lpimm and the Nyquist frequency iscaused by sampling and the aliased noise componentsshown in Fig. 14. Still, due,to the absence of triangularnoise, the DQE of a CCD-based imaging chain is muchbefter than that one of a plumbicon-based chain. Thus, con-siderable MTF restoration is possible without introducingunacceptably high noise levels. As shown in Fig. 13, thetotal system MTF has fallen to about 0.2 at 2 lp/mm. Ac-

1 ,0

0,8

|J. 0,6FE o,o

o,2

0,0

0.7

0.6

0.5

U 5 I -

xRil -------\ - ' . ^ XRl l+ CCD , , .

2q1Li.l

Lrr 0.4(1

a \ n 2

0.2

0 .1

spatial frequency Ip/mml

Fig. 16 DQE curves for 60 keV average beam energy of a Cslscreen, an XRll, and a total imaging chain with a 1 kx1 k-pixel CCDcamera.

Journal of Electronic lmaging / January 1999 / Vol. 8(1 ) / 1 3


cording to Eq. (8), and with DQE values of 0.65 at zerospatial frequency and 0.37 at 2 lp/mm, the MTF can berestored to about 0.75 at 2 lp/mm.

In summary, image quality can be improved with respectto three major points by the innoduction of CCD cameras:first, the excellent geomelrical stability of the sensor arrayimproves modalities like subtraction angiography, whereaccurate registration of several images with respect to eachother is important. This enables also better correction offixed pattern noise. Second, the MTF of a CCD camera isconsiderably better than the MTF of a pickup tube. Due tothe physical separation of pixels in a CCD, this holds alsofor low spatial frequencies. In a pickup tube, transfer of lowspatial frequency information can be reduced by, amongother effects, large-area equalization of the charge imageon the target during readout. Third, ttre absence of triangu-lar noise improves the SNR and DQE particularly forhigher spatial frequencies, thus allowing a higher degree ofdigital MTF restoration and edge enhancement. To stillkeep quantization noise negligible compared to the reducednoise levels particularly at higher spatial frequencies, 12 bitA./D conversion may be advisable rather than the previ-ously mentioned 8 or 10 bit conversion. Further advantagesof a CCD camera include its low sensitivity to electromag-netic interferences, and a mechanical construction which ismuch more compact than that of pickup tubes.

4 Solid-State Large Area Flat Dynamic X-Raylmage Detector (FDXD)

Despite the excellent image qualiry today's XRIfIV-camera chains achieve, there are some drawbacks of thesesystems. One is the bulkiness, size and weight particularlyof the XRII, which hampers especially bedside imag-gwith mobile fluoroscopy systems. Furthermore, the systemssuffer from geometric distortion, veiling glare and vignett-ing. Veiling glare refers to disrurbing light in the outputimages of an XRII caused by scatter of x-ray quanta, pho-toelectrons and light photons inside the XRII, which re-duces contrast. Vignetting denotes the drop in output imageintensity toward the circular image boundary, which iscaused by the convex shape of the XRtr input screen. Al-though both veiling glare and vignetting can be compen-sated digitally, it is preferable to prevent them in the firstplace.

This can be accomplished with an all solid-state imagesensor which does not rely on electron and light-opticalcomponents and therefore promises negligible vignettingand veiling glare, zero geometric distortion due to its rigidpixel matrix, and a flat input screen. In addition the devicescan be made compact and light-weight even for very largequadratic or rectangular field sizes up to 50X 50 cmz. Witha püel pitch about 100-200 pcm, and a very large dynamicrange, such a device is very well suited for high qualitydigital radiography. At the same time it can be used as afluoroscopy imager using a readout mode with reducedpixel count, obtained by either zooming or pixel binning.

The fabrication of large area solid-state image sensorshas now become feasible by the progress made in thin-filmeiectronics technology which has been developed for flatdisplays. A detector array is realized by a 2D matrix ofsensor elements as schematically depicted in Fig. 17. Eachsensor eiement consists of an amomhous silicon (a-Si)

14 / Journal of Electronic lmaging / January 1999 / Vol. 8(1)

Fig. 17 Schematic of the solid-state detector.

photodiode and a thin-fiim transistor (TFI).22 The array iscovered by a thallium-doped Csl-scintillator screen makingit sensitive to x radiation."

The main issues we will address are signal üansfer anddetector noise. The results show that the SNR of the devicecan be made sufficiently Iarge even at very low dose rates,despite the fact that there is no photoelectron amplificationstep involved.

4.1 Structure of the DetectorFigure 17 shows the detector setup: each pixel-formed bya photodiode and a TFT-is connected via a data line to acharge sensitive readout amplifier, and is linked by a gateline to a row driver. The photodiode sensitivity is spectrallymatched to the thallium-doped CsI layer, i.e., is highestbetween 550 and 600 nm, where thallium-doped CsI lightemission is strong. Via an analog multiplexer each readoutamplifier is connected to an A/D converter. The chargegenerated after illuminating the detector is read out by suc-cessive activation of the detector rows via the row drivers.The charge of an activated row is transferred to the readoutamplifiers, and subsequently digitized.

4.2 Signal Transfer and Noise

To analyze signal and noise behavior, we focus on fluoros-copy, which, due to the Iow doses used, is more criticalthan medium or high-dose radiography. The target is toachieve a fluoroscopy performance which is comparable orbetter than that of XRIVTV-camera chains. This means thatespecially for low doses electronic detector noise must besignificantly lower than quantum noise, which, aqsqlding toSec. 2, is also low at low doses.

In order to present quantitative figures on SNR perfor-mance achieved so far, we consider a l kXl kpixel detec-tor with 2OO p,m pitch and a corresponding Nyquist fre-quency of 2.5 lp/mm as described in Ref. 22.

Signal transfer is mainly characterized by the detectorgain G quantifying the conversion of x radiation into elec-


0 1 2 3 4spatial f requency lpimml

Fig. 18 Presampling MTF ol the solid-state detector.

ffon charge within each photodiode, and by the MTF. For agiven, typical fluoroscopy x-ray beam quality, the gain ismeasured in electrons generated in each pixel per nGy ofradiation incident on the anay. With an optical reflectorcoating on top of the CsI screen, which prevents the escapeof generated luminescence photons, values of G:700 electrons/nGy were measured for a protoq?e detec-tor in Ref. 22. In the meantime this value has been im-proved to about 1500 electrons/nGy by increasing the ac-tive size of the plgtodiodes and by optimizing the CsIdeposition process."

The presampling MTF for the analog detector compo-nents before sampling, i.e., the CsI screen and the finitepixel pitch, is shown in Fig. 18. As the presampling MTFdoes not vanish beyond the Nyquist frequency, some alias-ing of quantum noise will occur, similarly as described forCCD sensors in Sec. 3.4. With the MTF at Nyquist fre-quency having dropped to approximately I5Vo, the influ-ence of aliased noise is appreciable but not too severe.

The main electronic noise sources of this detector are thereadout amplifier noise and the reset noise of the pixel ca-pacitances. In order to relate the noise measurements to thesignal level, the noise standard deviation is in the followingalso expressed in electrons, and refers to a single pixel.

The effective amplifier noise depends on the readouttiming pattern. Our protofype is read out by so-called cor-relatid-double sampling (CbS) depicted in Fig. 19.22 Thegate of each TFT in a row is activated by the corresponding

H-gfr*tus"--|-o"tu L

Fig. 19 Timing of correlated double sampling. Sample 1 taken be-fore readout is subtracted from sample 2 which is taken after capaci-tive teedthrough has been reversed. The sampling aperture is aboutI lrs.

row driver through a positive pulse, which enables flow ofthe signal charge to the readout amplifier. To avoid distor-tion of the sampled charge signal by additional charge fedcapacitively through the TFT gate during the positive slopeof the activation pulse, sampling of the amplified chargesignal occurs only after the TFTs are deactivated again, i.e.,after the capacitive feedthrough has been reversed by thenegative slope of the activation pulse. From this sample,another sample is subtracted which was t*en before chargereadout. This readout timing scheme acts as a highpass fil-ter which efficiently suppresses offsets and a Iowpass noisecomponent of the amplifiers, which is known as 1f noise.Simultaneously, the finite sampling aperture of about 8 ,u.sacts as a lowpass filter attenuating white amplifier noise.

With this timing scheme the pixel capacitances' noise isgiven by ,lTkrc|, where I is the absolute temperature, kthe Boltzmann constant, and C, the pixel capacitancewhich is typically on the order of 2 pF.

4.2.1 Fluoroscopy pertormance

Let us now examine the potential signal-to-noise perfor-mance of a 1kxl k-pixel array with 2O0 p,m pitch at atypical fluoroscopic dose rate of 10 nGy/frame and an av-erage beam energy of 60 keV. At a gain G of 1500electrons/nGy, this generates a sign^al of 15 000 electronsper püel. With 4e:300 quanta/mm', the number of x-rayquanta Q absorbed per pixel is about 10. Hence, after de-tection the standard deviation of x-ray quantum noise perpixel is given by C1Q:+l+O electrons.

When using correlated double sampling, the standarddeviation of readout amplifier noise is about 600 electrons.The pixel capacitances' noise is about 800 electrons. Thesefigures result in an overall electronic noise with a standarddeviation of 1000 electrons.

Hence the SNR of the detector is clearly determined byquantum noise at typical fluoroscopic dose rates. Even indark image areas, where quantum counts are as Iow as oneper pixel, the quantum noise still is at 1500 elecffons, ex-ceeding the overall electronia noise.

Assuming a pixel size of 200X200 pmz, the corre-sponding values for XRII/TV-camera chains are a gain ofabout 10 000 electrons per 10 nGy and pixel, at an elec-tronic noise level of approximately 200 electrons. Thesefigures show that the electronic SNR performance of XRIVTV-camera systems will not quite be reached by the solid-state detector, but the difference should in practice be in-significant, due to the dominant x-ray quantum noise. Inaddition for the solid-state detector the absorption effi-ciency for the x-ray quanta can be further increased, henceincreasing the overall SNR for a given entrance dose.

4.3 Digital Processing

To achieve optimal detector performance, it is necessary tocompensate fixed pattern effects like variations in offsetand gain of the sensor elements by suitable digital process-ing. An additional effect which should be conected digi-tally is the memory effect, which denotes the remaining ofan undesired residual image after image readout. This iscaused by the incomplete flowing off of electrons from thephotodiodes. The memory effect is intrinsic to amorphous

Journal of Electronic lmaging / January 1999 / Vol. 8(1 ) / 1 5


silicon, and can be described by an appropriate model.2aBased on this model, digital compensation of the memoryeffect is feasible.

In conclusion, when taking into account the above-mentioned advantages of the solid-state detector of no geo-metric distortion, no veiling glare, and no vigneffing, weexpect that the overall image quality of these future x-rayimagers wiil be superior, provided that the best perfor-mance achieved in laboratory models so far can be trans-ferred to the production of clinical imaging devices.

5 Digital Quantum Noise Reduction

Regardless of whether one employs the described solid-state detector or the discussed XRII/TV-camera chain, fluo-roscopy images are always afflicted by relatively highquantum noise levels compared to signal due to the lowdose rates used. One possibility to reduce quanrum noise inthe observed images is by appropriate digital noise filtering.In fuIl frame rate fluoroscopy with 25 or more images persecond, this can be done by,recursive temporal averaging,what can be interpreted as digitally introducing an intendedlag. To prevent blurring of moving objects, filtering is re-duced or switched off entirely in areas where object motionis detected (mo tion adaptiv e' fiIterin g).25'26

For low frame rate fluoroscopy mentioned in Sec. 3.1,however, temporal filtering is often not feasible, so that theonly option which remains is spatial filtering within singleimages. Such an algorithm is described in the following.

To reduce noise, the filtering algorithm has to exploitstructural differences between signal content of images andnoise. Modelling of noise can be based on our previousdiscussions in Secs. 2 and3. However, appropriate model-ing of the signal content of medical images is difficult if notimpossible. The often used Markov random field models,for example, do not capture sufficient medical detail if keptmathematically tractable. It is therefore desirable to keepthe assumptions on the signal as weak as possible. Wehence rely here on a noise model as starting point and as-sume those input observations as containing image signal(in addition to noise) that cannot be explained well by noiseonly.

5.1 Noise Reduction by SpectralAmplitudeEstimation

We have aiready seen that quantum noise exhibits alowpass-shaped power spectrum in the acquired images. Arelatively high proportion of the overall noise power ishence contributed from low spatial frequencies' Standardspatial window-based filters, like lowpas-s convolution ker-nels, nonstationary Wiener approaches,'' or order statistic-based filters,28-30'5o*"u"r, tend to attenuate mainly highspatial frequency components. This has the twofold short-coming that, first, the full noise reduction potenrial is notexploited. Second, the filtering operation shifts the spectralcomposition of quantum noise even more towards low spa-tial frequencies, what is often visualiy unpleasilg despite areduction of the overall noise power. Additionally, orderstatistic-based filters tend to generate patches or streaks ofconstant intensity,3o'31 which add to the unnatural appear-ance of such processed images.

To avoid such artifacts without sacrificing noise reduc-tion performance, and in particular to be able to tailor our


20 40 60 lnl"n.n,

too 1:

Fig. 20 Noise power vs signal intensity for the fluoroscopy se-quence in Fig. 10. Also shown is the noise power which remainsafter filtering by DFT- and DCT-based spectral amplitude estimationwas applied.

filters to spatially coloured noise, we apply here the conceptof so-called spectral amplitude estimation, where noise at-tenuation is carried out in the spectral domain.32 Spectralamplirude estimation -is a widely reported approach tospeech restoration,"-ro but there are only few reported im-age processing applications." Starting with a decomposi-tion of the input images into overlapping blocks which aresubjected to a standard block transform [discrete fouriertransform (DFT) or discrete cosine transform (DCT)], thecentral idea is to compare each transform coefficient to thecorresponding "noise only" expectation, i.e., to its coun-terpart from the NPS. Each coefficient is then aftenuateddepending on how likely it is that it contzins only noise'The purpose of the block decomposition is to make thefilter algorithm adaptive to small image detail as well as tononstationarities of noise.

5.1.1 Quantum noise model

We have already seen that, due to its Poissonian nature, thequantum noise power depends linearly on the quantum flow

4e, that is, on signal. For the digitized fluoroscopy imageshown in Fig. 10, this dependence over image intensity isdepicted in Fig. 20. Over low to medium intensities, thiscurve exhibits (approximately) the predicted linear rise.The drop-off toward high intensities is caused by the re-duced amplifier gain for high signat amplitudes (white

compression, Sec. 3.2). Second, as already discussed andshown in, e.g., Fig. 15, quantum noise exhibits a lowpassshaped power spectrum in the acquired images. For a givenfluoroscopy system, both the signal dependence and theNPS of quantum noise are assumed to be known. Further-more, we assume that quantum noise is the dominatingnoise source (quanrum-limited imaging), and that the sys-tem MTF is signal independent. Signal dependence ofquantum noise then affects only the absolute scale of theNPS, but notits shape. We therefore separate signal depen-dence and spatial frequency dependence of the observedI.[PS Nz(S,&) by

o3o 3 0oLc

1 0

l r21S,a) : oz (S) r ' (u ) , (e)


Fig. 21 1D illustration of the use of overlapping windowed blocksover a spatial coordinate k to prevent blocking artifacts in processedimages. The periodically repeated window function w(k) adds up tounity, thus allowing perfect reconstruction of the original image. lfthe DFT is used, windowing serves the double tunction of allowingblock overlaps and preventing leakage.

where l(S; is the noise power which depends on signal Sas illustrated in, e.g., Fig. 20. The spatial frequency depen-dence or NPS shape is captured by the reference NPSn'(u), which integrates to unity.

As our spectral amplitude estimation filter is based onblock transforms like DFT or DCT, we estimate the NPSby well-known periodogram averaging techniques based onthe same block size and analysis window fype as the oneused later in the noise reduction algorithm. For a givensystem, the described estimation is done a priori from ho-mogeneous exposures like the ones used for Figs. 12 and15. Windowing serves here the double purpose of prevent-ing DFT leakage and enabling the use of overlappingblocks in order to avoid blocking artifacts in the processedimages (see Fig. 21). Signal dependence l1S; ana meNPS shape nz1u1 arc stored in look-up tables.

5.1.2 Spectral amplitude estimation filter

In the following, we denote the observed, noisy specüalcoefficients by Y (u) . To compare these observations towhat we would expect if only noise were present, we cal-culate the so-called instantaneous SNR r(z), which relatesthe instantaneors power of each observation l(rz) to theexpected noise power iD(a). The squared instantaneousSNR is given by

Fig. 22 Block diagram oJ the spectral amplitude estimation filter fornoise reduction.

After image decomposifion and DFT, the correspondingNPS coefficient N'(S,a) for each observation is read outfrom this box, where the mean block gray level Y(0) isused as an estimate for the signal intensity S needed toaccess the appropriate scaling factor fwe make here theapproximating assumption that the signal-dependent noiseis stationary within a block (short space station*ity)].o2(S). The SNR r(u) can now be calculated, and the cor-responding attenuation factor hlr(u)] is read out from the"attenuation function" box. Y(u) is then multiplied byhlr(u)1, before the noise reduced image is reconstructedby taking the inverse DFT, and reassembling the imageblocks.

The precise shape of the attenuation function is deter-mined by the chosen objective function and the underlyingmodels ior noise and signal.3a'3?'3e'40 Our filter algorithm iibased on the concept of minimum mean square error esti-mation of spectral amplitudes.32 The resulting attenuarionfunction is derived in Appendix B, and depicted in Fig. 23.

5.2 Processing Results

Figure 24 shows the enlarged central porfion of the fluoros-copy image in Fig. 10, and the filtered version is depictedin Fig. 25. This result was obtained using the DFT in con-nection with a blocksize of 64X.64 pixel and an overlap of16 pixel. The DFT window was a modified separable 2D, . . l Y t r ) l tr - \ u t :

o ( r )(10)

where (an estimate for) @(a) is easily obtained from theNPS in Eq. (9): estimation of the NPS by periodogramaveraging involvel normalization by the squaresum of win-dow coefficients."''o Simply dropping this normalizationyields the desired estimate for O(n). Noise reducfion isachieved by attenuating each observation I(u) dependingon r27u1 according to

S ( r ) : Y ( u ) h \ r ( u ) ) . ( 1 1 )

The attenuationfunction lr(r) varies between zero and one,and increases monotonically over r. The total effect is anattenuation of spectral coefficients which are likely to rep-resent mainly noise. Generally, the attenuafion function isreal valued. Equation (11) therefore is a zero-phase filter,hence the name spectral amplitude estimation.

Figure 22 shows the block diagram of the noise filter.The box termed "noise model" stores tie signal depen-dence of quantum noise and the reference NPS of Eq. (9).

0.8

0.7

0.6

t

Io

o

o6

3 4SNR (r)

Fig. 23 Attenuation h as function of the instantaneous SNR r, de-rived based on the concept of minimum mean square error estima-t ion.

Journal of Electronic lmaging / January 1999 / Vol. 8(1) / 17


Fig. 24 Enlarged portion of the image in Fig. 10.

Hanning window, whose cosine-shaped drop-off was re-stricted to a 16 pixel wide border region. The noise powerremaining after filtering is still signal dependent, and quan-titatively evaluated in Fig. 20, showing a noise power re-duction by about 607o.

DCT based processing results are hardly distinguishablefrom those obtained using DFT. As shown in Fig. 20, quan-titative noise reduction performance is also similar to theDFT-based processing. One advantage of the DCT is itsnegligible leakage. Windowing before taking the transformcan hence be omitted. Block overlap is now only necessaryto avoid the block raster from becoming visible, what canbe ensured by overlaps as low as two pixels, reducing thecomputational load by about 4OVa. The window operationrequired by block overlap is now performed within the im-age reconstruction box inFig.22.

A processing result for another image (Fig. 26) is shownin Fig. 27. This result was obtained by a modified spectral

Fig, 25 Noise-reduced version of Fig. 24.

18 / Joumal of Electronic Imaging / January 1999 / Vol. 8(1 )

Fig. 26 Part of a low dose x-ray image, showing a thin guidewireinserted into a patienfs vascular system.

amplitude estimation algorithm which explicitly detects andexploits perceptually important oriented structures, likeguide wires, catheters, or edges of bones.al When using theDFT, the occurrence of an oriented structure in an imageblock results in the spectral domain in a concentration ofenergy along the line perpendicular to the spatial orienta-tion and passing through the origin. For each image block,our modified algorithm uses an inertia matrix-based methodto detect the line along which concentration of energy isstrongest.*""' The filter then explicitly adapts to the de-tected orientation by applying less attenuation to---or byeven enhancing-coefficients along this line, with this be-havior beine the more pronounced. the more distinct thelocal orientätion.ot Cor."rpondingly, the processed imageshows both strong suppression of noise and enhancement ofIines and edges, like the guide wire. Another example of afluoroscopy image is shown in Fig. 28, and the processingresult in Fig. 29. Unlike the previous image, this example

Fig. 27 Figure 26 processed by orientation-dependent noise reduc-t ion and enhancement.


o - ' -

E 3tr1 2.5

I

1 . 5

1

Fig. 28 Part of a fluoroscopy image depicting intestines.

contains no sharp guide wires, but is dominated bymedium-sharp anatomic strucfures like fissures and thetransition from intestines to background, which are alsoenhanced.

To relate the achieved noise power reduction to potentialdegradations of the MTF during filtering, we have alsomeaswed the SNR before and after filtering. Our filter be-ing adaptive implies, of course, that its performance is de-pendent on the input signal. For our measurements, wesimulated different versions of a "difficult" image of a thinguidewire embedded in quantum noise. corresponding toacquisitions at 10, 30, and 100 nGy, respectively. For eachsimulated acquisition dose, the ratio of the SNR after fil-tering to the SNR before filtering is depicted over spatialfrequency in Fig. 30. fl-oosely speaking, this ratio could be

Fig.29 Figure 28 processed by orientation-dependent noise reduc-tion and enhancement.

0 0.2 0.4 0.6 0.8 1 1"2spatial frequency (lpimm)

Fig. 30 Ratio of SNR after processing to SNR before processing asa function of spatial frequency. Measurements based on 30 realiza-tions of a simulated test image containing a thin guidewire andquantum noise corresponding to acquisit ions at 10, 30, and 100nGy.

interpreted as a (signal dependent) DQE of the filter.] Themeasurements were based on 30 realizations of each testimage. Evidently, the SNR is indeed improved over a widerange of spatial frequencies, i.e., potential losses of MTFare outweighed by the reduction of noise power.

5.3 DiscussionThe strength of our spectral domain approach to quantumnoise reduction is that it can be tailored specifically to theknown properties of quantum noise, while only very gen-eral assumptions about the behavior of the unlrrrown signalunder orthogonal transforms are required.

It might appear as a shortcoming of the discussed algo-rithms that processing is based on an unnatural block struc-ture. In the present context, however, blockwise processinghas the significant advantage that inevitable "decision" er-rors, especially mistaking noise for signal, are dispersedover entire blocks as sine-like gratings. The occasional ap-pearance of these gratings can easily be concealed by re-taining a low wideband noise floor. The visually muchmore unpleasing patchJike artifacts of spatial domain fil-ters are thus completely avoided. The block raster itself isprevented from becoming visible through the use of over-lapping blocks. The advantage of the DCT-based filter isthat it keeps the computational overhead to a minimum,whereas the DFT provides a framework well suited for theexploitafion of local orientation.

6 Concluding Remarks

This article described selected topics of medical x-ray im-age acquisition and processing by digital techniques, someof which are already well established, while others are pres-ently emerging. By first comparing digital radiography sys-tems to analog ones, it was shown that a key advantage ofdigital imaging lies in the inherent separation of image ac-quisition and display media, which enables one to digitallyrestore and enhance acquired images before they are dis-played. It turned out that the amount of restoration andenhancement which can be applied is fundamentally lim-ited by noise. The performance of digital imaging systemswas therefore characterized bv the sisnal-to-noise ratio and

Journal of Electronic Imaging / January 1999 / Vol. B(1 ) / 1 I


related measures. Expressing the SNR in terms of x-rayquantum flow resulted in the two pnncipal performancemeasures, viz., noise equivalent quanta (NEQ and detec-tive quantum efficiency (DQE) Essentially, these measuresquantify how effectively the incoming quantum flow is ex-ploited by an imagrng system at different spatial frequen-cies.

The relation between signal and noise transfer was em-phasized in our subsequent discussions, starting withpresent-day fluoroscopy systems based on x-ray imageintensifier/camera chains. We highlighted the fundamentaldifferences in noise behavior between vacuum cameratubes and CCD cameras, and discussed the major pointswhere image quality can be improved by the introductionof CCD cameras. We then presented a concept for a flatsolid-state x-ray detector based on amorphous silicon,which is intended to be used for both high resolution radi-ography and fluoroscopy. Here, we analyzed signal transferand noise properties for the more critical application tolow-dose fluoroscopy and showed that this concept can in-deed be a viable alternativerto XRIVTV systems. Presentdevelopment efforts, however, focus on the introduction ofthis and other flat detector tvpes into the market for disitalradiography.a3'a Oth". nat äetector types include a-Siae-tectors with direct diode switching without using TFTs,a5'46and detectors using amorphous selenium (a-Se) to detect xradiation, which are read out by TFT matrices.4T'48 Finally,we described a new noise reduction algorithm specificallytailored to the reduction of x-ray quantum noise in low-dose x-ray images, where the SNR is especially low. As apurely spatial filter, this algorithm is particularly suited forlow frame rates often used in connection with pulsed fluo-roscopy, where temporal filtering is often not feasible.

Appendix A

To see that the power spectral density N| of quantum noiseis given by the quantum flow qe, consider an ideal detectorwhich counts quanta impinging on an area A. The detectedsignal then obeys S:qsA. Due to the Poissonian nature ofquantum noise, S is aiso identical to the noise power o2 atthe detector output. The impulse response /(x) of this de-tector is

I t i f x e A ,f("):

I o else,

where x is the spatial coordinate. The noise power can alsobe calculated from

(42)

Hence, Ni:eo.

Appendix B

The MMSE estimate Sia; of the noise-free spectral coef-

ficient S(u) is given by the conditional mean S1r;:E[S(a)lY(u)), and explicit ly exploits the well-knownsignal energy compaction properties of both the DFT and

20 / Joumal of Electronic lmaging / January 1999 / Vol. 8(1)

the DCT. Assuming for each block that the undistorted im-age signal appears in only a few coefficients, each observedcoefficient represents either noise only (null hypothesis116), or signal and noise (alternative hypothesis F11). Splirt ing up A[S(r)lY(r.r)] according to these hypotheses, weclearly have E[S(a)ly(u),Ao]:0. The conditional meancan then be rewritten tcr

S(u) : r ls ( , ) lv ( r ) l: r [ s (a ) lY (u ) ,H ] . (1 -P {äg lY ( " ) l ) , (B l )

where Prff/sly(r)] is the probabiliry for the null hypoth-esis given Y(a). Furthennore, based on the single observa-tion I(a) comrpted by zero-mean noise, and with no fru-ther prior knowledge available, we haveE[s(a) lY(u) ,H] :Y(u) . Using the Bayes ru le,P.[HolY(u)] cu be rewritten to

Pr [Hs lY(u) ] :plrfu)lrsl.k(Ho)

pLvtu)l

with p[f (a)1116] denoting the probability density function(pdf) for the noisy observation when signal is absent. Theunconditional pdf p[y(a)] can be split up into

plY ( u) l : p lY ( u) l H s l Pr( ao )

(82)

+ p lY (u ) lH 1 l . ( I - P r (äo ) ) .

Equation (B1) can now be rewritten to

. I a f r ( a ) l a o J . P r ( H o ) l ( ' )s (a ) : r fu ) } *

o l ra lWr l . Pr ( Hr ) l

(Ar) pty(ülnst:;;*{ +#]

^ l ( l v t u ) l 2 l r - ls ( u ) : r t a ) [ t + t t e x n l - . ( r , i j ,

with

Since each spectral coefficient is a weighted sum of thegray levels in the processed block, we assume the coeffi-cients as complex Gaussian distributed according to thecenüal limit theorem. For the null hypothesis, i.e., when theobservation I(u) is caused by noise only, this complexGaussian pdf is given by

(B3)

(84)

^ ^ f *t ' : N i

I _ f2(x tdx:N24.

(Bs)

where ö(a) is the noise variance defined in Sec. 5.1. ForY(a) given hypothesis Hy, i.e., when signal is present,another complex Gaussian pdf can be assumed with un-known variance. Typically, however, the variance P(u) ofcoefficients containing both signal and noise is much largerthan <D(a). Inserting the complex Gaussian pdfs into Eq.(Ba), the following expression for the estimate can then bederived:

(B6)

Digital x+ay imaging

. P(u)Pr(H6)Ä : -" <D(u)Pr(F11) (87)

Finally, we introduce a weighting factor a for the noisevariance. similarly as done in, e.g., generalized Wienerfilters."' We then obtain

. | [ ' 2 ( r ) l \ . 'S( , ) : v tu )11+f , exp l - - l | : y@)h l r (u ) ) ,

\ t d l l(88)

where r(u) is the instantaneous SNR of Eq. (10), andhlr(u)l the MMSE attenuation function. The quantiry \ isthe (noninstantaneous) signal-plus-noise to noise ratioweighted by h(Hs)/Pr(I11). As the precise values ofP(u), k(Hs) and Pr(II1) are unloown, we regard \ as afree parameter to be selected externally, similarly as done,e.g., with regularization parameters in regularized imageprocessing paradigms. Experimentally, we found that ),:1.5 and a:3.0 gave good processing results. The corre-sponding attenuation function is depicted in Fig. 23.

Acknowledgments

This work was performed while all authors were with Phil-ips Research Laboratories, Aachen, Germany. We thank M.Weibrecht and C. Mayntz for fruitful discussions.

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Til Aach received the diploma and Doc-toral degree in electrical engineering fromAachen University of Technology (RWTH)in 1987 and 1993, respectively. From 1987to 1993, he was with the Institute for Com-munications Engineering, Aachen Univer-sity of Technology, where he was respon-sible for a number of research oroiects inmedical image processing, anälyiis andcompression of stereoscopic images, and

ia' image sequence analysis. From 1993 to1998, he was a project leader with Philips Research Laboratories,Aachen, where he was responsible tor projects in medical image

processing. In 1996, he was also a lecturer with Otto-von-GuerickeUniversity, Magdeburg. As ol February '1998, he was appointed afull professor of computer science and head of the lnstitute for Sig-nal Processing and Process Control, Medical University of Luebeck,Germany. He is also a consultant to industry.

Ulrich Schiebel received his PhD in phys-ics from Justus-Liebig-University, Giessen,Germany in 1975. Since 1978 he is withPhilips Research Laboratories, Aachen,Germany. For more than 15 years he hasbeen working in the field of electronic x-raydetectors for digital radiography, deliveringmajor research contributions to theselenium-based Philips Thoravision sys-tem and a-Si:H flat-panel x-ray imagers.Currentlv he is a department head in Phil-

ips Research, responsible for the fields of luminescent materials andelectron emitters.

Gerhard Spekowius studied physics atthe University of Hannover (Germany) andreceived a PhD in 1991 . His majorf ields ofworking have been multiple molecular ion-ization processes, photionization, laserspectroscopy, and charged particle detec-tors. In 1992 he joined the Phil ips Re-search Laboratories in Aachen. Since thenhe has been working as project leader fordigital x-ray imaging with XRlI/CCD cam-era chains and x-ray image quality model-on medical disolavs and soft-copv imaqeing. His current focus is on medical displays and soft-copy image

presentation.


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