Relaxed ordered subsets algorithm for image restoration of confocal microscopy

The expectation-maximization (EM) algorithm for maximum-likelihood image recovery converges very slowly. Thus, the ordered subsets EM (OS-EM) algorithm has been widely used in image reconstruction for tomography due to an order-of-magnitude acceleration over the EM algorithm. However, OS-EM is not guaranteed to converge. The recently proposed ordered subsets, separable paraboloidal surrogates (OS-SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence. In this paper, we develop a relaxed OS-SPS algorithm for image restoration. Because data acquisition is different in image restoration than in tomography, we adapt a different strategy for choosing subsets in image restoration which uses pixel location rather than projection angles. Simulation results show that the order-of-magnitude acceleration of the relaxed OS-SPS algorithm can be achieved in restoration. Thus the speed and the guarantee of the convergence of the OS algorithm is advantageous for image restoration as well.