Algorithms for simultaneous sparse approximation. Part II: Convex relaxation

By Joel A. Tropp. Signal Processing, 2006

803 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/61017d4ea4aaa53f78b4dddbf29db65d62d9f811

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In Biomedical Engineering

In Computational Mechanics

In Signal Processing

Citations in the corpus

An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem (2007, methodology): “Other variants involve replacing the row-wise norm with the norm [50] and the norm [5].”
Sparse Representation for Signal Classification (2006, methodology): “Detailed analysis of this pursuit algorithm can be found in [20, 21].”
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors (2006, background): “The problem of MMV can also be considered as how to achieve sparse representations for single-measurement vectors (SMVs) simultaneously [4]–[6].”
A Survey of Sparse Representation: Algorithms and Applications (2015, methodology): “In the literature [23, 24], from the perspective of spar e problem modeling and problem solving, sparse decompositio n algorithms are generally divided into two sections: greedy algorithms and convex relaxation algorithms.”
Accelerating SENSE using compressed sensing (2009, methodology): “With distributed CS algorithms (34-36), all aliased images with common sparse support may be simultaneously reconstructed using fewer samples.”
A Convex Feature Learning Formulation for Latent Task Structure Discovery (2012, background): “Such situations arise in several real world applications (Tropp, 2006; Jalali et al., 2010).”
Fully-Adaptive Feature Sharing in Multi-Task Networks with Applications in Person Attribute Classification (2016, background): “This problem is NP-hard, however, there exist approaches based on convex relaxation [41] and greedy simultaneous orthogonal matching pursuit (SOMP) [42] which can produce approximate solutions.”
Spatially Sparse Precoding in Millimeter Wave MIMO Systems (2013, background): “combining problems via orthogonal matching pursuit, the problems in (17) and (24) can be solved by leveraging other algorithms for simultaneously sparse approximation [47].”
Differential Sparse Coding (2008, background): “Priors which produce sparse solutions for W , especially L1 regularization, have gained attention because of their usefulness in ill-posed engineering problems [1], their ability to elucidate certain neuro-biological phenomena, [2, 3], and their ability to identify useful features for classification”
Robust Recovery of Signals From a Structured Union of Subspaces (2008, background): “Prior work on recovery of block-sparse vectors [24] assumed consecutive blocks of the same size.”
Online Learning for Matrix Factorization and Sparse Coding (2009, background): “d samples of an unknown probability distribution, but are structured in groups (which are however independent from each other), and one may want to address the problem of simultaneous sparse coding, which appears also in the literature under various names such as group sparsity or grouped variable s”
The null space property for sparse recovery from multiple measurement vectors (2011, neutral): “, references [12], [9], [21], [23]–[24].”
Sparse Subspace Clustering: Algorithm, Theory, and Applications (2012, background): “Hence, minimizing (28) corresponds to minimizing the number of nonzero rows of C [61], [62], [63], i.”