Blind deconvolution with non-smooth regularization via Bregman proximal DCAs

Blind deconvolution is a technique to recover an original signal without knowing convolving filter. It naturally formulated as minimization of quartic objective function under some assumption. Because its differentiable part does not have Lipschitz continuous gradient, existing first-order methods are theoretically supported. In this paper, we employ the Bregman-based proximal methods, whose convergence guaranteed L-smooth adaptable (L-smad) property. We first reformulate difference convex (DC) functions and apply Bregman DC algorithm (BPDCA). This decomposition satisfies L-smad The method extended BPDCA with extrapolation (BPDCAe) for faster convergence. When our regularizer has sufficiently simple structure, each iteration solved in closed-form expression, thus algorithms solve large-scale problems efficiently. also provide stability analysis equilibriums demonstrate proposed through numerical experiments on image deblurring. results show that BPDCAe successfully recovered outperformed other algorithms.