Abstract
Image deblurring is formulated as an unconstrained minimization problem, and its penalty function is the sum of the error term and TVp-regularizers with0<p<1. Although TVp-regularizer is a powerful tool that can significantly promote the sparseness of image gradients, it is neither convex nor smooth, thus making the presented optimization problem more difficult to deal with. To solve this minimization problem efficiently, such problem is first reformulated as an equivalent constrained minimization problem by introducing new variables and new constraints. Thereafter, the split Bregman method, as a solver, splits the new constrained minimization problem into subproblems. For each subproblem, the corresponding efficient method is applied to ensure the existence of closed-form solutions. In simulated experiments, the proposed algorithm and some state-of-the-art algorithms are applied to restore three types of blurred-noisy images. The restored results show that the proposed algorithm is valid for image deblurring and is found to outperform other algorithms in experiments.
Highlights
Over the past half century, image deblurring has been intensively studied and extensively applied in many fields, such as biometric identification, remote sensing, and video surveillance, among others
The proposed SBMTVp is employed to restore the blurred-noisy images in Figure 2 to verify its effectiveness
The algorithms in [3, 7] are introduced for comparison in terms of restoring the same blurrednoisy images to verify the superiority of SBMTVp
Summary
Over the past half century, image deblurring has been intensively studied and extensively applied in many fields, such as biometric identification, remote sensing, and video surveillance, among others. As an ill-posed and inverse problem, image deblurring requires a stable solution For this purpose, Tikhonov et al [1] propose regularization technology that initially uses ‖Cu‖22 as the regularizer, with C as the Tikhonov operator. The TV-regularizer has been employed by many state-of-the-art image deblurring algorithms [3,4,5], but recent research reveals that for modeling the sparseness of image gradient, the lp-norm (‖ ⋅ ‖pp) with. From the nonconvexity and nonsmoothness of TVpnorm, imaging inverse problems involving TVp-regularizer or lp-regularizer are generally confronted with challenges in the existence of solutions and low efficiencies of corresponding algorithms. Variable splitting technology has recently been proposed and extensively applied to inverse problems [10, 11], including TVp-regularized image deblurring problems [12]. The proposed algorithm is empirically found to converge to satisfactory solutions with only several iterations, as verified by experiments
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