31 October 1997 Grouped coordinate descent algorithms for robust edge-preserving image restoration
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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.
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Jeffrey A. Fessler, "Grouped coordinate descent algorithms for robust edge-preserving image restoration", Proc. SPIE 3170, Image Reconstruction and Restoration II, (31 October 1997); doi: 10.1117/12.279713; https://doi.org/10.1117/12.279713
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