Fast fully 3-D image reconstruction in PET using planograms

• Published in: IEEE transactions on medical imaging 2004-04, Vol.23 (4), p.413-425
• Main Authors: Brasse, D., Kinahan, P.E., Clackdoyle, R., Defrise, M., Comtat, C., Townsend, D.W.
• Format: Article
• Language: English
• Subjects: Algorithms; Biomedical imaging; Computer Simulation; Detectors; Engineering Sciences; Feasibility Studies; Filters; Fourier Analysis; Fourier transforms; Gamma Cameras; Image Enhancement - instrumentation; Image Enhancement - methods; Image Interpretation, Computer-Assisted - instrumentation; Image Interpretation, Computer-Assisted - methods; Image reconstruction; Imaging, Three-Dimensional - instrumentation; Imaging, Three-Dimensional - methods; Life Sciences; Positron emission tomography; Radiology; Reconstruction algorithms; Reproducibility of Results; Sensitivity and Specificity; Sensor arrays; Signal Processing, Computer-Assisted; Tomography, Emission-Computed - instrumentation; Tomography, Emission-Computed - methods; Transducers; Two dimensional displays
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2004.824231

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.