The cosparse analysis model and algorithms
The cosparse analysis model and algorithms
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DOI：
10.1016/j.acha.2012.03.006
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发表时间：
2013-01-01
影响因子：
2.5
通讯作者：
Gribonval, R.
中科院分区：
文献类型：
--
作者：
Nam, S.;Davies, M. E.;Gribonval, R.
经过十年对稀疏表示综合模型的广泛研究，我们可以有把握地说，这是一个成熟而稳定的领域，具有明确的理论基础和吸引人的应用。除了这种方法之外，还有一种分析对应模型，尽管它与综合替代方案相似，但却明显不同。令人惊讶的是，分析模型并没有得到类似的关注，今天对它的理解是肤浅和片面的。在本文中，我们仔细研究了分析方法，更好地将其定义为信号的生成模型，并将其与合成模型进行对比。这项工作提出了有效的追求方法，旨在解决反问题正则化的分析模型之前，伴随着其性能的初步理论研究。我们在几个实验中证明了分析模型的有效性，并提供了一个详细的研究与二维有限差分分析算子，一个密切的表弟的电视规范的模型。(C)2012 Elsevier Inc. All rights reserved.
After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial.In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments, and provide a detailed study of the model associated with the 2D finite difference analysis operator, a close cousin of the TV norm. (C) 2012 Elsevier Inc. All rights reserved.