Fast PET image reconstruction based on SVD decomposition of the system matrix

Data filtering based on matrix pseudo-inverse is a well-known but not yet a ppreciated means of tomographic image reconstruction. In the present work, the feasibility of image reconstruction based on singular value decompositi on (SVD) of the system matrix for animal two-dimensional positron emission tomography is demonstrated. Analytic detector response function accounting for the noninvariant spatial system response is explicitly included into th e system matrix. Regularization of the SVD-based solution with the singular spectrum truncation (TSVD solution) derived from spatial resolution analys is is proposed. TSVD reconstruction is fast except for the matrix decomposi tion step, which is performed once for a given scanner geometry. Reconstruc ted image quality and quantitation are compared to those obtained with filt ered backprojection (FBP) and iterative maximum likelihood technique. With the constant progress of computing power, TSVD image reconstruction may bec ome a viable alternative to FBP for routine clinical applications.