·
Ray projections are formed by
scanning a thin cross section of the body with an XR beam and measuring the
transmitted radiation with a radiation detector.
·
The detector adds up the energy
from the all the transmitted photons
·
The numerical data from
multiple ray sums are then computer-processed to reconstruct an image.
C: 301-307
·
A crossectional / slice is
divided into many tiny blocks (voxels) each assigned a number (m or HU)
proportional to the degree that the block attenuated – N = NOe-mx - the XR beam (determined by their composition, thickness and beam
quality)
·
As more blocks are placed in
the path of the beam more equations are required to determine the individual
block values – this is performed by computerized algorithms that solve the
equations as quickly as possible
·
There are many methods of image
reconstruction:
o
Simple back projection:
§ Summation method
§ Oldest method – mainly historical
§ See fig 19-13 and 19-14 C:304-304
o
Iterative methods:
§ Simultaneous reconstruction
§ Ray-by-Ray Correction
§ Point-by-Point Correction
o
Analytical methods:
§ 2D Fourier analysis
·
Any function of time or space
can be represented by the sum of various frequencies and amplitudes of sine and
cosine waves
·
See fig 19-17 C:307
§ Filtered back projection
·
Similar to back projection
except that the image is filtered (modified) to counterbalance the effect of
sudden density changes, which create blurring in simple back projection.
·
The frequencies responsible for
blurring are eliminated to enhance more desirable frequencies
BB: 346-357
·
Rays and views:
o
The number of rays (the number
of single transmission measurements made
by a single detector at a given moment) used to reconstruct a CT image has a
profound influence on the radial component of spatial resolution and the number
of views (represents the projection angles made up of a number of rays) affects
the circumferential component of the resolution
o
Reducing the ray sampling
reduces the resolution (blurred image)
o
Too few views – causes view
aliasing – objects with a high spatial frequency (sharp edge) produce radiating
artifacts more apparent at the periphery
·
Preprocessing:
o
Calibration of collected data
from “air scans” – adjustment of the electronic gain of each detector in an
array
o
Variation of detector efficiencies
is corrected
o
The logarithm of the signal is
then computed to acquire an attenuation coefficient for each voxel by using
reference data and data from each ray
·
Interpolation/ interleaving:
o
Fig 13-25 BB:350
o
Most algorithms assume an XR
source having negotiated a circular path around the patient – Helical CT
scanning has a helical trajectory
o
To compensate for the differing
acquisition geometry the helical data is interpolated into a series of planar
image data sets.
o
Essentially it is a weighted
average of the data from either side of the reconstruction plane
o
It importantly enables
reconstruction at any point along the length of the scan to within ½
(pitch)(slice thickness) of each edge of the scanned volume
o
Allows production of additional
overlapping images with no additional dose.
o
Helical scanning and
interleaved reconstruction allows placement of additional images along the
patient so that the clinical examination is almost uniformly sensitive to
subtle abnormlities (fig 13-26 BB:351)
o
NB: images with a 5mm slice
thickness on helical scanners can be reconstructed every 1 mm BUT this does not
mean that 1mm spatial resolution is achieved.
§ I.e. SAMPLING PITCH is 1 mm BUT SAMPLING APERTURE is 5 mm
·
Simple back projection:
o
Planar projection data sets
must now be used to reconstruct the individual tomographic images
o
Modern CT – 205,000 pixels
(512x512) and each of the 800,000 projections (1000 views and 800 rays/ view)
represents an individual equation therefore computer uses backprojection
o
Based on trigonometry –
designed to emulate the acquisition process in reverse
o
Each ray represents an
individual measurement of m.
o
In addition to the value of m for each
ray the reconstruction algorithm “knows” the acquisition angle and position in
the detector array corresponding to each ray.
o
Simple back projection starts
with and empty matrix and the for m value from each
ray in all views is smeared or backprojected onto the imge matrix (the value of
m is added to each pixel in a line through the image corresponding to
the ray’s path – but this produces blurring (fig 12-28 BB:352)
·
Filtered backprojection
o
The raw data are mathematically
filtered before backprojection – this reverses the image blurring, restoring
the image to an accurate representation of the object.
o
Involves convolving the
projection data with a convolution kernel – the kernel refers to the shape of
the filter function in the spatial domain, whereas it is common to perform the
filtering in the frequency domain.
o
The spatial domain data is
converted to the frequency domain, is then filtered and then returned to the
spatial domain for backprojection.
o
Various convolution filters can
be used to emphasize different characteristics in the CT image.
·
Bone kernels and soft tissue
kernels:
o
Bone kernels accentuate higher
frequencies in the image at the expense of increased noise – High contrast
(high signal) so SNR is inherently quite good – therefore these images can
afford a slight decrease in the SNR in return for sharper detail in the bone
regions
o
Where high spatial resolution
is less NB than high contrast – to see metastatic disease – soft tissue kernels
are used ----- lower noise but lower spatial resolution
·
HU
o
CT(HU)XY = 1000 x (mXY - mwater)/mwater
