总变分与重叠组稀疏性用于在脉冲噪声下的图像去模糊
Total variation with overlapping group sparsity for image deblurring under impulse noise
AI总结：
本文提出一种结合总变分与重叠组稀疏性的模型，用于在脉冲噪声下恢复模糊图像，通过引入盒约束和ADMM框架下的高效算法，有效缓解阶梯效应并提升PSNR和相对误差。
摘要：
总变分（TV）正则化方法是图像去模糊中保留边缘的有效方法。然而，基于TV的解决方案通常存在阶梯效应。本文为了缓解阶梯效应，提出了一种新的模型，用于恢复受脉冲噪声影响的模糊图像。该模型包含一个ℓ1保真项和一个总变分与重叠组稀疏性（OGS）正则化项。此外，我们对所提模型施加盒约束以获得更准确的解决方案。提出了一种高效的算法，在交替方向乘子法（ADMM）框架下求解该模型。我们使用一个内循环，嵌套在主要化最小化（MM）迭代中，用于所提方法的子问题。与其他方法相比，数值结果表明，所提方法在避免阶梯效应和PSNR以及相对误差（ReE）方面显著提高了恢复质量。
英文摘要：
The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect, we propose a new model for restoring blurred images with impulse noise. The model consists of an $\ell_1$-fidelity term and a TV with overlapping group sparsity (OGS) regularization term. Moreover, we impose a box constraint to the proposed model for getting more accurate solutions. An efficient and effective algorithm is proposed to solve the model under the framework of the alternating direction method of multipliers (ADMM). We use an inner loop which is nested inside the majorization minimization (MM) iteration for the subproblem of the proposed method. Compared with other methods, numerical results illustrate that the proposed method, can significantly improve the restoration quality, both in avoiding staircase effects and in terms of peak signal-to-noise ratio (PSNR) and relative error (ReE).
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