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A Non-Convex Optimization Technique for Sparse Blind Deconvolution -- Initialization Aspects and Error Reduction Properties by Adiga, Aniruddha; Seelamantula, Chandra Sekhar is a scholarly article available to read on EtoBox.

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Sparse blind deconvolution is the problem of estimating the blur kernel and sparse excitation, both of which are unknown. Considering a linear convolution model, as opposed to the standard circular convolution model, we derive a sufficient condition for stable deconvolution. The columns of the linear convolution matrix form a Riesz basis with the tightness of the Riesz bounds determined by the autocorrelation of the blur kernel. Employing a Bayesian framework results in a non-convex, non-smooth cost function consisting of an $\ell_2$ data-fidelity term and a sparsity promoting $\ell_p$-norm ($0 \le p \le 1$) regularizer. Since the $\ell_p$-norm is not differentiable at the origin, we employ an $\epsilon$-regularized $\ell_p$-norm as a surrogate. The data term is also non-convex in both the blur kernel and excitation. An iterative scheme termed alternating minimization (Alt. Min.) $\ell_p-\ell_2$ projections algorithm (ALPA) is developed for optimization of the $\epsilon$-regularized cost function. Further, we demonstrate that, in every iteration, the $\epsilon$-regularized cost function is non-increasing and more importantly, bounds the original $\ell_p$-norm-based cost. Due to non

Author

Adiga, Aniruddha; Seelamantula, Chandra Sekhar

Published

2017

Language

EN