基于加权L1/2范数和TV正则化的图像去噪方法
Weighted L1/2 Norm with TV Regularization for Image Denoising
摘要: 面对被严重稀疏噪声损坏的观测数据，采用L1范数来度量稀疏性的低秩恢复算法已不能很好的从退化的观测矩阵中恢复低秩结构。本文提出了一个新的加权低秩矩阵恢复算法用于图像去噪。利用L1/2范数来度量稀疏性，引入权重分配给每个组成元素，并结合Lp范数特定情况下(p = 1/2)的封闭阈值算子，提出加权的L1/2正则化，相比常用的L1范数更加有效。同时将TV正则化整合到我们的方法中，有效的保证了图像的边缘特征。所提的方法与现有的低秩恢复算法相比，在增强图像结构平滑性和去除大的稀疏噪声方面表现更好，图像重建的质量有了明显提高。
Abstract: In the face of the observation data damaged by serious sparse noise, the low-rank restoration algo-rithm using L1 norm to measure sparsity can not better recover the low-rank structure from the degraded observation matrix. In this work, a new weighted low-rank matrix restoration algorithm is proposed for image denoising. The L1/2 norm is used to measure sparsity, and the weight is as-signed to each component element. Combined with the closed threshold operator of Lp norm (p = 1/2), the weighted L1/2 regularization is proposed, which is more effective than the common L1/2 norm. At the same time, TV regularization is integrated into our method to effectively ensure the edge features of the image. Compared with the existing low-rank restoration algorithm, the pro-posed method has better performance in enhancing the smoothness of image structure and remov-ing large sparse noise, and the quality of image reconstruction has been significantly improved.
文章引用：吴万红, 吴自凯. 基于加权L1/2范数和TV正则化的图像去噪方法[J]. 应用数学进展, 2023, 12(1): 6-14. https://doi.org/10.12677/AAM.2023.121002

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