Image deblurring is a fundamental problem in imaging field which often needs to recover the important structure of images. This paper addresses the image deblurring problem by considering an image as a combination of its cartoon (the piecewise smooth part of the image) and texture (the oscillation part of the image) components. To recover both of these parts, we propose the use of coupled analysis-based sparse representations to regularize the cartoon structure and the texture part of the image. We apply anisotropic total variation with a quadratic term to enhance the edges existing in the cartoon part. Furthermore, we develop a multivariable Bregman optimization method to solve the proposed image restoration model by combining the alternating minimization method and the split Bregman iteration. The experiments show that the proposed algorithm not only performs well for image decomposition, but also outperforms the previously established methods in terms of the visual residual error, the structure similarity index and the peak signal-to-noise ratio for image deblurring.

中文翻译：

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使用 Bregmanized 稀疏正则化和各向异性全变的形态分量图像恢复

图像去模糊是成像领域的一个基本问题，往往需要恢复图像的重要结构。本文通过将图像视为其卡通（图像的分段平滑部分）和纹理（图像的振荡部分）组件的组合来解决图像去模糊问题。为了恢复这两个部分，我们建议使用基于耦合分析的稀疏表示来规范卡通结构和图像的纹理部分。我们应用具有二次项的各向异性总变化来增强卡通部分中存在的边缘。此外，我们开发了一种多变量 Bregman 优化方法，通过将交替最小化方法和分裂 Bregman 迭代相结合来解决所提出的图像恢复模型。