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Baraniuk, Richard G.; DeVore, Ronald A.; Kyriazis, George; Yu, Xiang

doi:10.1023/a:1014554317692

Cited by 22 publications

(1 citation statement)

References 9 publications

(2 reference statements)

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“…Otherwise, the CSSA solves the problem by condensing the nonmonotonic segments of the tree branches via an iterative sort-andaverage scheme during a greedy search through the nodes. For further details, see Baraniuk and Jones (1994), Baraniuk (1999), Baraniuk (2002). The tree-based CS scheme is outlined as follows.…”

Section: Compressed Sampling (Cs)mentioning

confidence: 99%

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

2014

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This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT.

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Section: Compressed Sampling (Cs)mentioning

confidence: 99%

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

2014

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High‐frequency subband compressed sensing MRI using quadruplet sampling

Sung

Hargreaves

2012

Magnetic Resonance in Med

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Purpose To presents and validates a new method that formalizes a direct link between k-space and wavelet domains to apply separate undersampling and reconstruction for high- and low-spatial-frequency k-space data. Theory and Methods High- and low-spatial-frequency regions are defined in k-space based on the separation of wavelet subbands, and the conventional compressed sensing (CS) problem is transformed into one of localized k-space estimation. To better exploit wavelet-domain sparsity, CS can be used for high-spatial-frequency regions while parallel imaging can be used for low-spatial-frequency regions. Fourier undersampling is also customized to better accommodate each reconstruction method: random undersampling for CS and regular undersampling for parallel imaging. Results Examples using the proposed method demonstrate successful reconstruction of both low-spatial-frequency content and fine structures in high-resolution 3D breast imaging with a net acceleration of 11 to 12. Conclusion The proposed method improves the reconstruction accuracy of high-spatial-frequency signal content and avoids incoherent artifacts in low-spatial-frequency regions. This new formulation also reduces the reconstruction time due to the smaller problem size.

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Structured Sparsity: Discrete and Convex Approaches

Kyrillidis

Baldassarre

Halabi

et al. 2015

Compressed Sensing and Its Applications

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Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated structured sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.

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Cited by 22 publications

References 9 publications

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

High‐frequency subband compressed sensing MRI using quadruplet sampling

Structured Sparsity: Discrete and Convex Approaches

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