BMED-4800/ECSE-4800Introduction to

Subsurface Imaging Systems

Lecture 5: X-ray Imaging (cont.)Kai E. Thomenius1 & Badri Roysam2

1Chief Technologist, Imaging Technologies, General Electric Global Research Center

2Professor, Rensselaer Polytechnic Institute

Center for Sub-Surface Imaging & Sensing

Review of Last Lecture

• Quick historical review of X-rays was given.• Block diagrams, key components defined.• Brief discussion of x-ray scattering• An X-ray beam, traversing through an object, is

attenuated by the exponential Lambert-Beer Law.• The product of the attenuation coefficient and the path

length of the x-ray beam in such a target is critical in establishing detectability.

• Today: – Digital Detectors, X-ray Metrics

Outline of Course Topics

• THE BIG PICTURE– What is subsurface imaging?– Why a course on this topic?

• EXAMPLE: Projection Imaging – X-Ray Imaging– Computer Tomography

• COMMON FUNDAMENTALS– Propagation of waves– Interaction of waves with

targets of interest 

• PULSE ECHO METHODS– Examples

• MRI– A different sensing modality

from the others– Basics of MRI

• MOLECULAR IMAGING– What is it?– PET & Radionuclide Imaging

• IMAGE PROCESSING & CAD

www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf

Digital Detector Front End

www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf

Detector Details

www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf

Selenium based Detector

www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf

Performance Metrics

Signal-to-noise Ratio (SNR)• SNR determines the

detectability of an object• Signal derived from x-ray

quanta• Noise comes from a

variety of sources:– X-ray quantum statistics,

Poisson distribution– Electronic noise– Sampling noise– Anatomical noise

• Signal processing steps critical to image quality– Correction for detector

variability, defects– Post-process filtering

FP vessel12 mm large cell lung cancer

Quantum noise• For a digital x-ray detector

system with square pixels– if the average number of

x-rays recorded in each pixel is N,

– then the noise (per pixel) will be

• Statistical distribution associated with x-rays is the Poisson distribution.– The above relation falls

out directly from this fact.

N

Poisson Distribution• Poisson Distribution is a probability

distribution given by

!

exp,k

kfk

If the expected no. of occurrences in a space is, then the probability that there are exactly k occurrences is given by f(k,)

Signal-to-noise ratio• The signal-to-noise ratio (SNR) is given by

• When the number of x-rays, N, is increased, the radiation dose also increases.

• To double the SNR, the dose to the patient needs to be increased by a factor of 4

• Contrast-to-noise ratio (CNR) for any two intensities (I1 and I2) at a detector is given by

– Here N is the nominal value of photons reaching the detector.

NNNN

SNR

CNR I1 I2

I1 I2

N

Other Measures of Image Quality

• Limiting Spatial Resolution (LSR)– The highest frequency that can be visualized

• Modulation Transfer Function (MTF)– Measures how the detector passes signal, as a function of

spatial frequency

MTF = Modulation at detector outputModulation at detector input

Spatial Frequency (cycles/mm)

MTF 1.0

00.03 - 0.05

LSR

MTF=1

in

out

ContrastContrastMTF

in out

q(x)

2A(f))

q(x)

2A(f))

Source: http://203.64.251.39/info/download/etc/breastx/93/93-04.ppt

MTF=0.5

• Modulation Transfer Function (MTF) / Spatial resolution:An imaging system’s ability to render the contrast of an object as a function of object detail.

in

out

ContrastContrastMTF

in out

q(x)

2A(f))

I(x)

2Aout(f)

MTF

Modulation Transfer Function•LSR– Screen-film has LSR » 20 lp/mm

• corresponds to 25 m pixel• Digital (GE) 100 m pixel

•Sources of MTF degradation– Lateral spread of light in scintillator

• limited by CsI needles• increases with scintillator

thickness– Lateral spread of secondary x-rays

• not significant away from k-edges of Cs and I

– Sampling aperture of pixel: sinc(fx*a)sinc(fy*a)

Spatial Frequency (cycles/mm)

MTF

Digital Imager

Film-Screen

If film’s LSR is better than digital why do we see improved performance in digital?

MTF For Direct, Indirect, and Screen Film

Measures of Image Quality-DQE

• Detective Quantum Efficiency, DQE

• SNR gives the transfer function of both signal and noise

DQE = SNR2 at detector output

SNR2 at detector input

SNR2 at detector output

Patient Dose

DQE

Spatial Frequency (cycles/mm)

DQE

Digital Imager

Film-Screen

1.0

High DQE in low-to-mid frequencies aids detection.High DQE in high frequencies aids characterization.

The higher the DQE,the higher the SNR,and the greater theprobability of detection.

where f is the spatial frequency (lp/mm), X is the exposure (mR) and :

S = Median Signal Level (cts), i.e. amplitude of information

MTF = Modulation Transfer Function

NPS = Noise Power Spectrum (cts^2 * mm^2)

C = Incident Xray Fluence (xrays / (mm^2 * mR)

DQE describes the measured SNR in relation to an ideal detector.

SNR2 is deduced from the ratio of MTF^2 (signal^2) to the NPS (noise^2)

DQE : Definition

www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf

Calibration of Digital Detector

•Dark Image Offset

•Diode leakage•FET charge

retention•Electronic

noise

Calibration of Digital Detector

•Offset Corrected Dark Image

•Electronic Noise

Calibration of Digital Detector

•Offset Calibrated

•Amplifier gainvariation

•Pixel-to-pixel gain variation

Calibration of Digital Detector

•Offset and Gain calibratedFlood exposed image

•Poisson statistical x-ray noise

•Electronic noise

Apply Corrections• Low dose: before and After Offset

Correction

Apply Corrections

• High dose

Tomosynthesis

Advanced Applications• Tomosynthesis- 3D X-ray

3D Breast Imaging - Tomosynthesis

• 3D imaging addresses the major problem with mammography today – superimposed tissue

• 3D imaging may enable compression reduction– Tissue immobilization vs. compression– Compliance with screening protocols

• Single tomo exam in MLO position may replace conventional mammography, potentially enabling dose reduction

Tomosynthesis Concept

Prototype System Parameters

• Prototype based on GEMS Senographe DMR, Revolution flat panel detector, motorized tube motion assembly

• 11 projections over +/- 25 degrees • 7.5 sec patient exam time• Total dose

– 1.5x a single mammographic view– 0.75x a standard mammographic screening

exam• 100 micron pixels• 1 mm (3d) slice separation

Tomosynthesis•Goal:• Limited 3-D reconstruction to remove

overlying/underlying structure• All image planes visualized using a single

acquisition

•Acquisition:• Vertical tube motion • Total tube angle: 5 -15°• Number of Projected Images: 15 – 25• Exam length: 5 -10 sec (single breath-

hold)• Slice thickness: ~1 cm• Enabled by GE Revolution™ detector:

Courtesy of Duke University and Wake Forest Medical Center

Rotational Axis

Tube vertical motion

Small Changes to Rad System allows for 3D Imaging!

Image Reconstruction in Tomo

• Data incompleteness– From a CT perspective, data is very sparse– Limited angular range (z-resolution)– Insufficient angular sampling (streaks)– Truncated projections (inconsistency)

Reconstruction Concept – Shift and Add

Add

Reconstruction of single plane

Projections at different angles

Shift

Vertical slice through object

Reconstruction of vertical slice through object

Artifacts: Out-of-plane structures appear as N low-contrast copies (N = # of projections). Contrast / “blurring” of artifacts depends on N, projection angles / tube trajectory, etc.

An Example…Standard 2D

x-ray

Images courtesy of Dr. Dan Kopans- MGH

Tomosynthesis – Missed Cancer

Spiculated Lesion

Standard MammogramMLO

Tomo SliceMLO

Tomosynthesis

Images courtesy of Dr. Dan Kopans- MGH

An Example…

3D Tomosynthe

sis

Images courtesy of Dr. Dan Kopans- MGH

Rad Tomo Example

Low Dose 3D Imaging!

Receiver Operating Characteristics

Receiver Operating Characteristic (ROC) curves

• Most basic task of the diagnostician is to separate abnormal subjects from normal subjects

• In many cases there is significant overlap in terms of the appearance of the image– Some abnormal patients have normal-looking films– Some normal patients have abnormal-looking films

• ROC curves are a tool for assessing the performance of a hypothesis testing algorithms.

2 x 2 Decision MatrixActually

AbnormalActually Normal

Diagnosed as

Abnormal

True Positive

(TP)

False Positive

(FP)Diagnosed as Normal

False Negative

(FN)

True Negative

(TN)

ROC curves (cont.)

• For a single threshold value and the population being studied, a single value for TP, TN, FP, and FN can be computed

• The sum TP + TN + FP + FN will be equal to the total number of normals and abnormals in the study population

• “True” diagnosis must be determined independently, based on biopsy confirmation, long-term patient follow-up, etc.

Summary•Design of digital x-ray detectors was

described.•Performance metrics (MTF, DQE) for x-

ray performance were given.– Justification for digital detectors was based

on these.•Tomosynthesis concept introduced.•Brief review of ROC methods for

hypothesis testing was given.

•Next time: Introduction to CT Scanners

Homework

• Using web resources (or sources given below), describe the key steps of the direct conversion process with amorphous Selenium. How are x-rays converted to electrons?

• What is the relative performance (MTF or DQE) with respect to the CsI-Photodiode approach?

• Which would you buy and why?– http://www.dondickson.co.uk/download/Challenges_

of_Direct_Digital_Radiology.pdf– Hoheisel et al., “Modulation transfer function of a

selenium-based digital mammography system”, IEEE Proc. Nuclear Science Symposium, 2004, 3589-3593

Instructor Contact Information

Badri RoysamProfessor of Electrical, Computer, & Systems EngineeringOffice: JEC 7010Rensselaer Polytechnic Institute110, 8th Street, Troy, New York 12180Phone: (518) 276-8067Fax: (518) 276-6261/2433Email: roysam@ecse.rpi.eduWebsite: http://www.ecse.rpi.edu/~roysabm Secretary: Laraine Michaelides, JEC 7012, (518) 276 –

8525, michal@rpi.edu

Instructor Contact Information

Kai E ThomeniusChief Technologist, Ultrasound & BiomedicalOffice: KW-C300AGE Global ResearchImaging TechnologiesNiskayuna, New York 12309Phone: (518) 387-7233Fax: (518) 387-6170Email: thomeniu@crd.ge.com, thomenius@ecse.rpi.edu Secretary: TBD