Grouped Coordinate Descent Algorithms for Robust Edge-Preserving Image Restoration

Abstract

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 non-negativity constraints and arbitrary neighborhood structures. Implementation in Matlab is remarkably simple, requiring no cumbersome line searches or tolerance parameters.