THE APPROXIMATE INVERSE AND CONJUGATE-GRADIENT - NONSYMMETRICAL ALGORITHMS FOR FAST ATTENUATION CORRECTION IN SPECT

Hybrid methods have been known for a long time as very efficient algor ithms for attenuation correction in single-photon emission computed to mography, but only recently have efforts been made to formulate them w ith more rigorous mathematics. This has allowed us to explain their ef ficiency in terms of approximate inversion, and to establish a converg ence condition. The present study focuses on the convergence problem a nd emphasizes the question of symmetry. Hybrid method operators ate no t symmetrical; therefore the convergence condition is not easily verif ied. New schemes based on a modified conjugate gradient method are pre sented. Convergence is proved and performances are shown to be at leas t as good as the standard hybrid schemes on perfect and noisy simulate d data.