Minggu, 20 November 2011

CT reconstruction


·         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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