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 appreciated means of tomographic image reconstruction. In the present work, the feasibility of image reconstruction based on singular value decomposition (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 the system matrix. Regularization of the SVD-based solution with the singular spectrum truncation (TSVD solution) derived from spatial resolution analysis is proposed. TSVD reconstruction is fast except for the matrix decomposition step, which is performed once for a given scanner geometry. Reconstructed image quality and quantitation are compared to those obtained with filtered backprojection (FBP) and iterative maximum likelihood technique. With the constant progress of computing power, TSVD image reconstruction may become a viable alternative to FBP for routine clinical applications.