Sparse solutions to linear inverse problems with multiple measurement vectors

By Shane F. Cotter, Bhaskar D. Rao, Kjersti Engan, Kenneth Kreutz-Delgado. 2005

1,455 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

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Citations in the corpus

Co-Occurrence Feature Learning for Skeleton Based Action Recognition Using Regularized Deep LSTM Networks (2016, methodology): “In the third term, for each group of units, a structural (cid:96) 21 norm, which is deﬁned as (cid:107) W 2 , 1 = i j w 2 i,j (Cotter et al. 2005), is used to drive the units to select a conjunction of descriptive inputs (joints/features) since the (cid:96) 21 norm can encourage the matrix W xβ,k…”
Modern regularization methods for inverse problems (2018, background): “[134, 119, 129, 317]) There are several relevant extensions of sparsity priors to multidimensional systems, in particular in a synthesis type formulation u = ∑”
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors (2006, neutral): “A precedent is Lemma 1 in Cotter et al. [1].”
Multitask Compressive Sensing (2009, methodology): “Typical approaches include the S-OMP algorithm in [12], [14], [18], the M-OMP algorithm in [13], the convex relaxation algorithm in [15], [18], and the M-BP algorithm in [13], among others.”
Probabilistic Multi-Task Feature Selection (2010, background): “Compressed sensing can be extended to the multiple measurement vector (MMV) model in which the signals are represented as a set of jointly sparse vectors sharing a common set of nonzero elements [7, 6, 23].”
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].”
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.”
Sparse Bayesian multi-task learning for predicting cognitive outcomes from neuroimaging measures in Alzheimer's disease (2012, methodology): “Regression was performed separately on each cognitive task (MMSE, RAVLT, or TRAILS) using the MRI measures as predictors, where the proposed T-MSBL-FP method and all the competing methods (T-MSBL, M-FOCUSS, Mixed ℓ2/ℓ1, S-OMP, RIDGE, MT-CS) were evaluated.”
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.”
Dictionary Learning Algorithms for Sparse Representation (2003, background): “Since our initial investigations into the properties of FOCUSS as an algorithm for providing sparse solutions to linear inverse problems in relatively noise-free environments (Gorodnitsky et al., 1995; Rao, 1997; Rao & Gorodnitsky, 1997; Gorodnitsky & Rao, 1997; Adler et al., 1996; Rao & Kreutz-Delg”
$\ell_{p}-\ell_{q}$ Penalty for Sparse Linear and Sparse Multiple Kernel Multitask Learning (2011, background): “For instance, the signal processing community have considered this kind of penalties either for sparse single or multiple signal approximations [ 12 ], [28].”
Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation (2009, methodology): “Several alternative methods have been proposed, that have polynomial complexit y [47], [45], [22], [13], [11], [30], [20], [21], [30].”
Structured Compressed Sensing: From Theory to Applications (2011, background): “Optimization based algorithms relax the norm in (32) and attempt to recover by mixed norm minimization [17], [112], [114]–[117]: subject to (34) for some ; values of and have been advocated.”
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals (2009, methodology): “Then, the frame V is constructed and the MMV is solved using simultaneous orthogonal matching pursuit [31], [32].”
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].”
Block-Sparse Signals: Uncertainty Relations and Efficient Recovery (2009, methodology): “In [28] extensions of the CoSaMP algorithm [29] and of iterative hard thresholding [30] to the model-based setting, which includes block-sparsity as a special case, are proposed and shown to exhibit provable recovery guarantees and robustness properties.”