Algorithms for large scale singular value analysis of spatially variant tomography systems

The problem of determining the eigenvalues of large matrices occurs often in the design and analysis of modern tomography systems. As there is an interest in solving systems containing an ever-increasing number of variables, current research effort is being made to create more robust solvers which do not depend on some special feature of the matrix for convergence (e.g., block circulant), and to improve the speed of already known and understood solvers so that solving even larger systems in a reasonable time becomes viable. Our standard techniques for singular value analysis are based on sparse matrix factorization and are not applicable when the input matrices ape large because the algorithms cause too much fill. Fill refers to the increase of non-zero elements in the LU decomposition of the original matrix A (the system matrix). So we have developed iterative solutions that are based on sparse direct methods. Data motion and preconditioning techniques are critical for performance. This conference paper describes our algorithmic approaches for large scale singular value analysis of spatially variant imaging systems, and in particular of PCR2, a cylindrical three-dimensional PET imager built at the Massachusetts General Hospital (MGH) in Boston. We recommend the desirable features and challenges for the next generation of parallel machines for optimal performance of our solver