Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising
Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising
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DOI：
10.4310/cms.2010.v8.n1.a6
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发表时间：
2011-04
期刊：
影响因子：
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通讯作者：
S. Osher;Yu Mao;Bin Dong;W. Yin
中科院分区：
文献类型：
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作者：
S. Osher;Yu Mao;Bin Dong;W. Yin
翻译后摘要：我们提出并分析了一个非常快速，高效和简单的方法。这种方法首先描述了更多的细节和严格的理论。其动机是压缩感知，现在有一个巨大的和令人兴奋的历史，这似乎已经开始与坎迪斯，多诺霍等人。我们的方法引入了一种改进称为“踢”的非常有效的方法，并将其应用到欠采样信号的去噪问题。开始使用Bregman迭代对图像进行去噪，并导致基于总变分的方法的结果得到改进。在这里，我们将其应用于去噪信号，特别是本质上稀疏的信号，甚至可能是欠采样的。
Abstract : We propose and analyze an extremely fast, efficient and simple method. This method was first described with more details and rigorous theory given. The motivation was compressive sensing, which now has a vast and exciting history, which seems to have started with Candes, Donoho, et.al. Our method introduces an improvement called "kicking" of the very efficient method and also applies it to the problem of denoising of undersampled signals. The use of Bregman iteration for denoising of images began and led to improved results for total variation based methods. Here we apply it to denoise signals, especially essentially sparse signals, which might even be undersampled.