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 highfrequency 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:
 ( x, y )   water
CT ( x, y )  1,000
 water
• 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
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):
SNR
D 3
T
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