Computed Tomography III

Reconstruction

Image quality

Artifacts

Simple backprojection

• Starts with an empty image matrix, and the value from each ray in all views is added to each pixel in a line through the image corresponding to the ray’s path

• A characteristic 1/r blurring is a byproduct

• A filtering step is therefore added to correct this blurring

Filtered backprojection

• The raw view data are mathematically filtered before being backprojected onto the image matrix

• Involves convolving the projection data with a convolution kernel

• Different kernels are used for varying clinical applications such as soft tissue imaging or bone imaging

Convolution filters

• Lak filter increases amplitude linearly as a function of frequency; works well when there is no noise in the data

• Shepp-Logan filter incorporates some roll-off at higher frequencies, reducing high-frequency noise in the final CT image

• Hamming filter has even more pronounced high-frequency roll-off, with better high-frequency noise suppression

Bone kernels and soft tissue kernels

• Bone kernels have less high-frequency roll-off and hence accentuate higher frequencies in the image at the expense of increased noise

• For clinical applications in which high spatial resolution is less important than high contrast resolution – for example, in scanning for metastatic disease in the liver – soft tissue kernels are used– More roll-off at higher frequencies and therefore produce

images with reduced noise but lower spatial resolution

CT numbers or Hounsfield units

• The number CT(x,y) in each pixel, (x,y), of the image is:

• CT numbers range from about –1,000 to +3,000 where –1,000 corresponds to air, soft tissues range from –300 to –100, water is 0, and dense bone and areas filled with contrast agent range up to +3,000

water

wateryxyxCT

),(

000,1),(

CT numbers (cont.)

• CT numbers are quantitative• CT scanners measure bone density with

good accuracy– Can be used to assess fracture risk

• CT is also quantitative in terms of linear dimensions– Can be used to accurately assess tumor volume

or lesion diameter

Digital image display

• Window and level adjustments can be made as with other forms of digital images

• Reformatting of existing image data may allow display of sagittal or coronal slices, albeit with reduced spatial resolution compared with the axial views

• Volume contouring and surface rendering allow sophisticated 3D volume viewing

Image quality

• Compared with x-ray radiography, CT has significantly worse spatial resolution and significantly better contrast resolution

• Limiting spatial resolution for screen-film radiography is about 7 lp/mm; for CT it is about 1 lp/mm

• Contrast resolution of screen-film radiography is about 5%; for CT it is about 0.5%

Image quality (cont.)

• Contrast resolution is tied to the SNR, which is related to the number of x-ray quanta used per pixel in the image

• There is a compromise between spatial resolution and contrast resolution

• Well-established relationship among SNR, pixel dimensions (), slice thickness (T), and radiation dose (D):

T

SNRD

3

2

Factors affecting spatial resolution

• Detector pitch (center-to-center spacing)– For 3rd generation scanners, detector pitch determines

ray spacing; for 4th generation scanners, it determines view sampling

• Detector aperture (width of active element)– Use of smaller detectors improves spatial resolution

• Number of views– Too few views results in view aliasing, most noticeable

toward the periphery of the image

Factors affecting spatial resolution (cont.)

• Number of rays– For a fixed FOV, the number of rays increases as

detector pitch decreases

• Focal spot size– Larger focal spots cause more geometric unsharpness

and reduce spatial resolution

• Object magnification– Increased magnification amplifies the blurring of the

focal spot

Factors affecting spatial resolution (cont.)

• Slice thickness– Large slice thicknesses reduce spatial resolution in the

cranial-caudal axis; they also reduce sharpness of edges of structures in the transaxial image

• Slice sensitivity profile– A more accurate descriptor of slice thickness

• Helical pitch– Greater pitches reduce resolution. A larger pitch

increases the slice sensitivity profile

Factors affecting spatial resolution (cont.)

• Reconstruction kernel– Bone filters have the best spatial resolution, and soft

tissue filters have lower spatial resolution

• Pixel matrix• Patient motion

– Involuntary motion or motion resulting from patient noncompliance will blur the CT image proportional to the distance of motion during scan

• Field of view– Influences the physical dimensions of each pixel

Factors affecting contrast resolution

• mAs– Directly influences the number of x-ray photons used to

produce the CT image, thereby influencing the SNR and the contrast resolution

• Dose– Dose increases linearly with mAs per scan

• Pixel size (FOV)– If patient size and all other scan parameters are fixed,

as FOV increases, pixel dimensions increase, and the number of x-rays passing through each pixel increases

Factors affecting contrast resolution (cont.)

• Slice thickness– Thicker slices uses more photons and have better SNR

• Reconstruction filter– Bone filters produce lower contrast resolution, and soft

tissue filters improve contrast resolution

• Patient size– For the same technique, larger patients attenuate more

x-rays, resulting in detection of fewer x-rays. Reduces SNR and therefore the contrast resolution

Factors affecting contrast resolution (cont.)

• Gantry rotation speed– Most CT systems have an upper limit on mA, and for a

fixed pitch and a fixed mA, faster gantry rotations result in reduced mAs used to produce each CT image, reducing contrast resolution

Beam hardening

• Like all medical x-ray beams, CT uses a polyenergetic x-ray spectrum

• X-ray attenuation coefficients are energy dependent– After passing through a given thickness of patient,

lower-energy x-rays are attenuated to a greater extent than higher-energy x-rays are

• As the x-ray beam propagates through a thickness of tissue and bones, the shape of the spectrum becomes skewed toward higher energies

Beam hardening (cont.)

• The average energy of the x-ray beam becomes greater (“harder”) as it passes through tissue

• Because the attenuation of bone is greater than that of soft tissue, bone causes more beam hardening than an equivalent thickness of soft tissue

Beam hardening (cont.)

• The beam-hardening phenomenon induces artifacts in CT because rays from some projection angles are hardened to a differing extent than rays from other angles, confusing the reconstruction algorithm

• Most scanners include a simple beam-hardening correction algorithm, based on the relative attenuation of each ray

• More sophisticated two-pass algorithms determine the path length that each ray transits through bone and soft tissue, and then compensates each ray for beam hardening for the second pass

Motion artifacts

• Motion artifacts arise when the patient moves during the acquisition

• Small motions cause image blurring

• Larger physical displacements produce artifacts that appear as double images or image ghosting

Partial volume averaging

• Some voxels in the image contain a mixture of different tissue types

• When this occurs, the is not representative of a single tissue but instead is a weighted average of the different values

• Most pronounced for softly rounded structures that are almost parallel to the CT slice

Partial volume averaging (cont.)

• Occasionally a partial volume artifact can mimic pathological conditions

• Several approaches to reducing partial volume artifacts– Obvious approach is to use thinner CT slices– When a suspected partial volume artifact occurs

with a helical study and the raw scan data is still available, additional CT images may be reconstructed at different positions