Theoretical Results on Sparse Representations of Multiple-Measurement Vectors

By Jie Chen, Xiaoming Huo. IEEE Transactions on Signal Processing, 2006

815 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/c26771ad7d22db288dae142fe0a892d31787cb06

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Citations in the corpus

On the Reconstruction of Block-Sparse Signals With an Optimal Number of Measurements (2008, background): “In [37,38,42,43] the authors use certain convex or non-convex relaxations (mostly different from the standard l1) and discuss their performances.”
Block-Sparse Signals: Uncertainty Relations and Efficient Recovery (2009, background): “Another interesting special case of the block-sparse model appears in the multiple measurement vector (MMV) problem, which deals with the measurement of a set of vectors that share a joint sparsity pattern [20], [21], [22], [14], [23].”
Sparse Bayesian multi-task learning for predicting cognitive outcomes from neuroimaging measures in Alzheimer's disease (2012, methodology): “Algorithms using this penalty include group Lasso (the variant used for the MMV model) [23], MMV based Basis Pursuit (M-BP) [4], and many domain-specific algorithms for feature extraction [13].”
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors (2008, methodology): “The system of (1) is called MMV in the literature when the joint sparsity prior holds over a finite set of sparse vectors [13], [14].”
Structured Compressed Sensing: From Theory to Applications (2011, background): “As shown in [110], [112], we can replace by in (31).”
Compressive Sensing-Based Adaptive Active User Detection and Channel Estimation: Massive Access Meets Massive MIMO (2019, background): “Compared to the conventional multiple measurement vector (MMV) problem [34], where identical pilots would be allocated to all pilot subcarriers, employing different pilot matrices across different pilot subcarriers can improve AUD and CE performance according to DCS theory [27].”
Spatially Common Sparsity Based Adaptive Channel Estimation and Feedback for FDD Massive MIMO (2015, methodology): “Applying the existing result for the MMV given in [26], (16) can be directly obtained.”
A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing (2014, methodology): “We can also combat the spectral library mutual coherence issue by using the multiple-measurement vector (MMV) formulation [53], which exploits the fact that in a given data set all the spectral vectors are generated by the same subset of library signatures, corresponding to the endmember signatures.”
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals (2009, methodology): “This challenge is referred to as a multiple measurement vectors (MMV) problem [28]–[33].”
Deep Networks for Direction-of-Arrival Estimation in Low SNR (2020, methodology): “CS techniques are generally separated into three main categories: a) on-grid, b) off-grid and c) grid-less methods [11], [12].”
Spatially Sparse Precoding in Millimeter Wave MIMO Systems (2013, methodology): “In the more general case of Ns > 1, the problem in (17) is equivalent to the problem of sparse signal recovery with multiple measurement vectors, also known as the simultaneously sparse approximation problem [45]–[48].”
A Survey of Sparse Representation: Algorithms and Applications (2015, background): “More detailed analysis on matching pursuit algorithms can be found in the literature [63].”
Robust Recovery of Signals From a Structured Union of Subspaces (2008, methodology): “The most detail ed theoretical analysis can be found in [28] which establishes equivalence results based on mutual coherence .”
Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference (2011, background): “1 Joint sparsity [28–32] in case of multiple time samples is utilized by assuming that sparse signals at all times are distributed with the same sparse prior.”
The null space property for sparse recovery from multiple measurement vectors (2011, neutral): “, references [13,11,24,27–29].”
Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals (2007, background): “Several sub-optimal efficient methods have been developed for this problem in the compressed sensing (CS) literature [15],[16].”
Sparse Methods for Direction-of-Arrival Estimation (2016, background): “x X. Since each row of Xcorresponds to one potential source, it is natural to deﬁne the sparsity as the number of nonzero rows of X, which is usually expressed as the following ‘ 2;0 norm (see, e.g., [20,77]): kXk 2;0 = #fn: kX nk 2 >0g= #fn: X n6= 0g; (38) where X ndenotes the nth row of X. Note”