For reconstructing a complex object wavefront from digital holograms, we propose a new penalized-likelihood approach based on the measurement statistics and edge-preserving regularization. The log-likelihood is complicated since the measurements are related to the magnitude of the complex beam. We use optimization transfer to derive a new simplified iterative algorithm that monotonically decreases the cost function. Unlike the conventional FFT-based holographic reconstruction method, the new approach uses all of the measured data and can be applied to holograms with any (known) reference beam pattern. Simulation results demonstrate the potential for improved image quality.

Iterative coordinate ascent algorithms have been shown to be useful for image recovery, but are poorly suited to parallel computing due to their sequential nature. This paper presents a new fast converging parallelizable algorithm for image recovery that can be applied to a very broad class of objective functions. This method is based on paraboloidal surrogate functions and a concavity technique. The paraboloidal surrogates simplify the optimization problem. The idea of the concavity technique is to partition pixels into subsets that can be updated in parallel to reduce the computation time. For fast convergence, pixels within each subset are updated sequentially using a coordinate ascent algorithm. The proposed algorithm is guaranteed to monotonically increase the objective function and intrinsically accommodates nonnegativity constraints. A global convergence proof is summarized. Simulation results show that the proposed algorithm requires less elapsed time for convergence than iterative coordinate ascent algorithms. With four parallel processors, the proposed algorithm yields a speedup factor of 3.77 relative to single processor coordinate ascent algorithms for a three-dimensional (3-D) confocal image restoration problem.

We introduce a new fast converging parallelizable algorithm for image restoration. This algorithm is based on paraboloidal surrogate functions to simplify the optimization problem and a concavity technique developed by De Pierro (1995) to simultaneously update a set of pixels. To obtain large step sizes which affect the convergence rate, we choose the paraboloidal surrogate functions that have small curvatures. The concavity technique is applied to separate pixels into partitioned sets so that parallel processors can be assigned to each set. The partitioned separable paraboloidal surrogates are maximized by using coordinate ascent (CA) algorithms. Unlike other existing algorithms such EM and CA algorithms, the proposed algorithm not only requires less time per iteration to converge, but is guaranteed to monotonically increase the objective function and intrinsically accommodates nonnegativity constraints as well.