Grouped coordinate descent algorithms for robust edge-preserving image restoration

We present a new class of algorithms for edge-preserving restoration of piecewise-smooth images measured in non-Gaussian noise under shift-variant blur. The algorithms are based on minimizing a regularized objective function, and are guaranteed to monotonically decrease the objective function. The algorithms are derived by using a combination of two previously unconnected concepts: A. De Pierro's convexity technique for optimization transfer, and P. Huber's iteration for M-estimation. Convergence to the unique global minimum is guaranteed for strictly convex objective functions. The convergence rate is very fast relative to conventional gradient-based iterations. The proposed algorithms are flexibly parallelizable, and easily accommodate nonnegativity constraints and arbitrary neighborhood structures. Implementation in Matlab is remarkably simple, requiring no cumbersome line searches or tolerance parameters.