The Cosparse Analysis Model and Algorithms
By Sangnam Nam, M. Davies, Michael Elad, Rémi Gribonval. arXiv.org, 2011
451 citations recorded by the source corpus.
Abstract 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.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/772b1ab30e55f174ad44098c57c29b275179188b
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In Nuclear and High Energy Physics
Citations in the corpus
- Deep Networks from the Principle of Rate Reduction (2020, methodology): “Under the assumption of the sparse generative model, if the convolution kernels {kc} match well with the “transpose” or “inverse” of the above sparsifying dictionaries, also known as the analysis filters (Nam et al., 2013; Rubinstein & Elad, 2014), signals in one class will only have high responses ”
- AMP-Net: Denoising-Based Deep Unfolding for Compressive Image Sensing (2020, methodology): “To solve this optimization problem, model-based recovery methods exploit some data structures by employing structure-inducing regularizers [5], such as sparsity in some transformation domains [6], [7], [8], [9], low rank [10], [11], [12], [13], [14], [15], and so on [16], [17], [18], [19], [20].”
- Dual Principal Component Pursuit (2015, methodology): “and variants of its relaxations have appeared on several occasions and in diverse contexts in the literature, but are much less understood than the now classic sparse [1] and cosparse [15] problems of the form”
- Compressed Sensing (2012, background): “The relation between these two minimization problems is far from being clear, and the recently introduced notion of co-sparsity [49] is an interesting approach to shed light onto this problem.”
- Learning Sparse FRAME Models for Natural Image Patterns (2014, methodology): “The proposed model (and the original FRAME model) is related to “analysis priors” developed in the last few years by the sparse modeling community [38] [13].”
- Sparse Regularization via Convex Analysis (2017, background): “For example, the idea may admit extension to more general convex regularizers such as total variation [48], nuclear norm [10], mixed norms [34], composite regularizers [1], [2], co-sparse regularization [40], and more generally, atomic norms [14], and partly smooth regularizers [61].”
- On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty (2011, background): “Algorithm (40) for problem (1) can also be used for signal recovery under analysis style sparsity requirements [26]: finding x with many (Ax)i equal to zero for a given frame operator A.”