· 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
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