### Augmented Bayesian Compressive Sensing

"... Abstract The simultaneous sparse approximation problem is concerned with recovering a set of multichannel signals that share a common support pattern using incomplete or compressive measurements. Multichannel modifications of greedy algorithms like orthogonal matching pursuit (OMP), as well as conv ..."

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Abstract The simultaneous sparse approximation problem is concerned with recovering a set of multichannel signals that share a common support pattern using incomplete or compressive measurements. Multichannel modifications of greedy algorithms like orthogonal matching pursuit (OMP), as well as convex mixed-norm extensions of the Lasso, have typically been deployed for efficient signal estimation. While accurate recovery is possible under certain circumstances, it has been established that these methods may all fail in regimes where traditional subspace techniques from array processing, notably the MUSIC algorithm, can provably succeed. Against this backdrop several recent hybrid algorithms have been developed that merge a subspace estimation step with OMP-like procedures to obtain superior results, sometimes with theoretical guarantees. In contrast, this paper considers a completely different approach built upon Bayesian compressive sensing. In particular, we demonstrate that minor modifications of standard Bayesian algorithms can naturally obtain the best of both worlds backed with theoretical and empirical support, surpassing the performance of existing hybrid MUSIC and convex simultaneous sparse approximation algorithms, especially when poor RIP conditions render alternative approaches ineffectual.

### SUPPLEMENTS M-SBL Implementation for Super-Resolution Microscopy using Speckle Illumination The

"... limits using speckle illumination and joint support recovery ..."

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### ,thenwecanfind remaining indices of supp with the generalized MUSIC criterion if

"... Abstract—There are a few corrections for the above titled paper (IEEE ..."

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### Article Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing

, 2015

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### Simultaneous Greedy Analysis Pursuit for Compressive Sensing of Multi-Channel ECG Signals

"... This paper addresses compressive sensing for multi-channel ECG. Compared to the traditional sparse signal recovery approach which decomposes the signal into the product of a dictionary and a sparse vector, the recently developed cosparse approach exploits sparsity of the product of an analysis matri ..."

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This paper addresses compressive sensing for multi-channel ECG. Compared to the traditional sparse signal recovery approach which decomposes the signal into the product of a dictionary and a sparse vector, the recently developed cosparse approach exploits sparsity of the product of an analysis matrix and the original signal. We apply the cosparse Greedy Analysis Pursuit (GAP) algorithm for compressive sensing of ECG signals. Moreover, to reduce processing time, classical signal-channel GAP is generalized to the multi-channel GAP algorithm, which simultaneously reconstructs multiple signals with similar support. Numerical experiments show that the proposed method outperforms the classical sparse multi-channel greedy algorithms in terms of accuracy and the single-channel cosparse approach in terms of processing speed.

### Average Case Analysis of High-Dimensional Block-Sparse Recovery and Regression for Arbitrary Designs

, 2015

"... This paper studies conditions for high-dimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the “block-sparse” case. In this regard, it first specifies conditions on the design matrix under which most of ..."

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This paper studies conditions for high-dimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the “block-sparse” case. In this regard, it first specifies conditions on the design matrix under which most of its block submatrices are well conditioned. It then leverages this result for average-case analysis of high-dimensional block-sparse recovery and regression. In contrast to earlier works: (i) this paper provides conditions on arbitrary designs that can be explicitly computed in polynomial time, (ii) the provided conditions translate into near-optimal scal-ing of the number of observations with the number of active blocks of the design matrix, and (iii) the conditions suggest that the spectral norm, rather than the column/block coherences, of the design matrix fundamentally limits the performance of computational methods in high-dimensional settings.

### Average Case Analysis of High-Dimensional Block-Sparse Recovery and Regression for Arbitrary Designs

"... Abstract This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the "block-sparse" case. In this regard, it first specifies conditions on the design matrix ..."

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Abstract This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the "block-sparse" case. In this regard, it first specifies conditions on the design matrix under which most of its block submatrices are well conditioned. It then leverages this result for average-case analysis of high-dimensional block-sparse recovery and regression. In contrast to earlier works: (i) this paper provides conditions on arbitrary designs that can be explicitly computed in polynomial time, (ii) the provided conditions translate into near-optimal scaling of the number of observations with the number of active blocks of the design matrix, and (iii) the conditions suggest that the spectral norm, rather than the column/block coherences, of the design matrix fundamentally limits the performance of computational methods in high-dimensional settings.