Subset-dependent relaxation in block-iterative algorithms for image reconstruction in emission tomography

This paper presents a row-action maximum likelihood algorithm (RAMLA), in which the relaxation parameter is controlled in such a way that the noise propagation from projection data to the reconstructed image is substantially independent of the access order of the input data (subsets) in each cycle of the sub-iterations. The 'subset-dependent' relaxation parameter lambda(k) (q) is expressed as lambda(k) (q) = beta(0)/(beta(0) + q + gammakM), where M is the number of angular views, q (0 less than or equal to q less than or equal to M - 1) is the access order of the angular view, k is the iteration number and beta(0) and gamma are constants. The constant beta(0) deals with the balance of the noise propagation and the constant y controls the convergence of iterations. The value of beta(0) is determined from the geometrical correlation coefficients among lines of coincidence response. The proposed RAMLA using the subset-dependent (dynamic) relaxation 'dynamic RAMLA (DRAMA)' provides a reasonable signal-to-noise ratio with a satisfactory spatial resolution by a few iterations in the two-dimensional image reconstruction for PET. Dynamic OS-EM (DOSEM) has also been developed, which allows the use of a larger number of subsets (OS level) M-sub without loss of signal-to-noise ratio as compared to the conventional OS-EM. DRAMA is a special case of DOSEM, where M-sub = M, and it is no more profitable to use DOSEM with a smaller M-sub (