On The Effect Of Relaxation In The Convergence And Quality Of Statistical Image Reconstruction For Emission Tomography Using Block-iterative Algorithms

Relaxation is widely recognized as a useful tool for providing convergence in block-iterative algorithms [1], [2], [6]. In the present article we give new results on the convergence of RAMLA (Row Action Maximum Likelihood Algorithm) [2], filling some important theoretical gaps. Furthermore, because RAMLA and OS-EM (Ordered Subsets - Expectation Maximization) [4] are the algorithms for statistical reconstruction currently being used in commercial emission tomography scanners, we present a comparison between them from the viewpoint of a specific imaging task. Our experiments show the importance of relaxation to improve image quality. © 2005 IEEE.20051320Ahn, S., Fessier, J.A., Globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms (2003) IEEE Trans. Med. Imag, 22, pp. 613-626Browne, J.A., Pierro, A.R.D., A row-action alternative to the em algorithm for maximizing likelihoods in emission tomography (1996) IEEE Trans. Med. Imag, 15, pp. 687-699E. S. Helou Nt. Teoria e experimentação com métodos incrementais relaxados em tomografia por emissão. M.Sc. Dissertation (in Portuguese), 2005Hudson, H.M., Larkin, R.S., Accelerated image reconstruction using ordered subsets of projection data (1994) IEEE Trans. Med. Imag, 20, pp. 601-609A. C. Kak and M. Slaney. Principles of Computerized Tomographic Imaging. IEEE Press, N. York, NY, 1999 (Electronic Copy)Nedić, A., Bertsekas, D.P., Incremental subgradient methods for nondifferentiable optimization (2001) SIAM J. Optim, 12, pp. 109-138Vardi, Y., Shepp, L.A., Kaufman, L., A statistical model for positron emission tomography (1985) Journal of the American Statistical Association, 80 (389), pp. 8-20. , Marc