Fast fully 3-D image reconstruction in PET using planograms.
We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space. Thus, backprojection of all the LORs passing through a point in the FOV corresponds to integration of a 2-D plane through the 4-D "planogram." The key step is that the integration along a set of parallel 2-D planes through the planogram, that is, backprojection of a plane of points, can be replaced by a 2-D section through the origin of the 4-D Fourier transform of the data. Backprojection can be performed as a sequence of Fourier transform operations, for faster implementation. In addition, we derive the central-section theorem for planogram format data, and also derive a reconstruction filter for both backprojection-filtering and filtered-backprojection reconstruction algorithms. With software-based Fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3-D backprojection and demonstrate a reduction in computation time by a factor of approximately 15.
Brasse
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Department of Radiology, University of Pittsburgh, Pittsburgh, PA 15213, USA.
Kinahan
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PE
Clackdoyle
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Defrise
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M
Comtat
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Townsend
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DW
D000465:Algorithms; D003198:Computer Simulation; D005240:Feasibility Studies; D005583:Fourier Analysis; D015902:Gamma Cameras; D007089:Image Enhancement / Q000295:instrumentation / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000295:instrumentation / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000295:instrumentation / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014055:Tomography, Emission-Computed / Q000295:instrumentation / Q000379:methods*; D014159:Transducers