Model-Based Compressive Sensing

Baraniuk, Richard G.; Cevher, Volkan; Duarte, Marco F.; Hegde, Chinmay

doi:10.1109/tit.2010.2040894

Cited by 1,403 publications

(1,599 citation statements)

References 45 publications

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“…The above analysis is heuristical and has been discussed in lots of literatures [9,10,11,12,13,14]. Meanwhile, algorithms exploiting the structures as well as the sparsity have been exhaustively investigated in the aforementioned literatures.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we focus on clustered sparsity model 2 , which is used in some applications where the significant coefficients of a sparse signal appear in clustered blocks. This kind of sparse pattern is often exploited in many concrete applications, such as multi-band signals, gene expression levels, source localization in sensor networks, MIMO channel equalization, magnetoencephalography [10,9,13].…”

Section: Introductionmentioning

confidence: 99%

“…The existing recovery algorithms for clustered sparsity model could be categorized into the following classes: 1) Block Greedy Algorithms [10,13];…”

Section: Introductionmentioning

confidence: 99%

“…To the best of the authors' knowledge, although all three classes of algorithms have taken into account the cluster prior, they also bring some new unknown parameters, such as the size and the number of the clusters, which, practically, are not easily obtained. For Class 1, Block-CoSaMP [10] and Block-OMP [13], the location of the clusters are fixed and the size (also the number) of clusters are required in the recovery procedure; for Class 2, the proposed algorithm in [12] does not require any information about the cluster prior except for the number of clusters; for Class 3, LaMP [11] the Matching Pursuit (MP) [15] procedure to carry out the sparse promoting. Additionally, it is worth noting that besides the cluster prior, sparsity information is necessary for all of the aforementioned algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian compressive sensing for cluster structured sparse signals

et al. 2012

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In traditional framework of Compressive Sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Other than sparse prior, structures on the sparse pattern of the signal have also been used as an additional prior, called modelbased compressive sensing, such as clustered structure and tree structure on wavelet coefficients. In this paper, the cluster structured sparse signals are investigated. Under the framework of Bayesian Compressive Sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms which are also taking into account the cluster prior, the proposed algorithm solves the inverse problem automatically -prior information on the number of clusters and the size of each cluster is unknown. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The existing recovery algorithms for clustered sparsity model could be categorized into the following classes: 1) Block Greedy Algorithms [10,13];…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian compressive sensing for cluster structured sparse signals

et al. 2012

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“…The main contribution of this paper is to exploit this mixture model as an underlying structure [6] so as to recover HSI with very few CS measurements. As opposed to our previous work [7], we assume that the mixture parameters A are unknown and we develop an algorithm to blindly learn this matrix A as well as the sources S from the CS measurements.…”

Section: Introductionmentioning

confidence: 99%

Distributed compressed sensing of Hyperspectral images via blind source separation

Golbabaee

Arberet

2010

2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers

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This paper describes a novel framework for compressive sampling (CS) of multichannel signals that are highly dependent across the channels. In this work, we assume few number of sources are generating the multichannel observations based on a linear mixture model. Moreover, sources are assumed to have sparse/compressible representations in some orthonormal basis. The main contribution of this paper lies in 1) rephrasing the CS acquisition of multichannel data as a compressive blind source separation problem, and 2) proposing an optimization problem and a recovery algorithm to estimate both the sources and the mixing matrix (and thus the whole data) from the compressed measurements. A number of experiments on the acquisition of Hyperspectral images show that our proposed algorithm obtains a reconstruction error between 10 dB and 15 dB less than other state-of-the-art CS methods.

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Compressive Optical Imaging: Architectures and Algorithms

Marcia

Willett

Harmany

2011

Optical and Digital Image Processing

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Many traditional optical sensors are designed to collect directly interpretable and intuitive measurements. For instance, a standard digital camera directly measures the intensity of a scene at different spatial locations to form a pixel array. Recent advances in the fields of image reconstruction, inverse problems, and compressive sensing (CS) [1,2] indicate, however, that substantial performance gains may be possible in many contexts via less direct measurements combined with computational methods. In particular, CS allows for the extraction of high-resolution images from relatively small focal plane arrays (FPAs). CS is described in detail in Chapter 23. The basic idea of CS theory is that when the image of interest is very sparse or highly compressible in some basis (i.e., most basis coefficients are small or zero valued), relatively few well-chosen observations suffice to reconstruct the most significant nonzero components. In particular, judicious selection of the type of image transformation introduced by measurement systems may significantly improve our ability to extract high-quality images from a limited number of measurements. By designing optical sensors to collect measurements of a scene according to CS theory, we can use sophisticated computational methods to infer critical scene structure and content.These ideas are particularly relevant to imaging applications in which it is useful or even crucial to keep the FPA of an optical system relatively small. For example, in low-light settings where sensitive detectors are costly, smaller FPAs translate directly to less expensive systems. Smaller FPAs also make systems lighter and, thus, more portable. In addition, imaging systems with fewer photodetectors consume less power and, therefore, require fewer battery charges. Finally, smaller cameras can fit into tighter spaces for unobtrusive surveillance. An important goal in the design of many imaging systems, then, is to extract as much information as possible from a small number of detector array measurements.While recent progress in the exploitation of CS theory is highly encouraging, there are several key issues in the context of optical systems that must be addressed:Optical and Digital Image Processing: Fundamentals and Applications, First Edition. Edited

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Model-Based Compressive Sensing

Cited by 1,403 publications

References 45 publications

Bayesian compressive sensing for cluster structured sparse signals

Bayesian compressive sensing for cluster structured sparse signals

Distributed compressed sensing of Hyperspectral images via blind source separation

Compressive Optical Imaging: Architectures and Algorithms

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