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Alternating Direction Method of Multipliers (ADMM) Based Deconvolving Images with Unknown Boundaries

K.Kalyani, K.Jansi Lakshmi, N.Pushpalatha

Deconvolution is an ill-posed inverse problem, it can be solvedby imposing some form of regularization (prior knowledge) on the unknown blur and original image.This formulation allows frame-based regularization. In several imaging inverse problems, ADMM is an efficient optimization tool that achieves state-of-the-art speed, by splitting the underlying problem into simpler, efficiently solvable sub-problems. In dconvolution the observation operator is circulant under periodic boundary conditions, one of these sub-problems requires a matrix inversion, which can be efficiently computable(via the FFT). we show that the resulting algorithms inherit the convergence guarantees of ADMM. These methods are experimentally illustrated using frame-based regularization; the results show the advantage of our approach over the use of the ―edgetaper‖ function (in terms of improvement in SNR).