Measuring Compton tomographic informational sufficiency using parallel-computed rank of system matrix
Compton gamma-ray scattering cameras promise to be a better alternative to PET or SPECT medical imaging for many applications. However, conventional designs for these cameras measure data that is not sufficient to satisfy completeness conditions for analytic image reconstruction. The literature proposes alternative designs that measure sufficient data to satisfy completeness conditions. As an alternative to the Central Slice Theorem for two-dimensional tomography, this thesis develops and applies software to calculate system matrix rank as a measure of the informational sufficiency for Compton cameras. A first set of software modules computes system matrices containing over 109 floating-point elements for discrete models of the conventional design and for an alternative design. A second set of modules verifies the correctness of the matrix computation by generating sets of measurements for a phantom image and then solving linear least squares using the Scalable Linear Algebra Package (ScaLAPACK) on multiple parallel computing nodes, comparing the result with the phantom. Another module finds the rank of the matrices by parallel-computing the Singular Value Decomposition (SVD) and tallying the effective singular values to determine the rank.