An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem

By David Paul Wipf, Bhaskar D. Rao. IEEE Transactions on Signal Processing, 2007

876 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Signal Processing

View Paper: https://www.semanticscholar.org/paper/f617c8c809639eff3a89c670edcee0139aaae3f2

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In Computational Mechanics

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Citations in the corpus

The Benefit of Group Sparsity (2009, background): “[11] and multi-task compressive sensing [4] from the Bayesian hierarchical modeling point of view.”
Multi-task compressive sensing with Dirichlet process priors (2008, methodology): “…exploiting the statistical relationships among the tasks, for example, Distributed Compressed Sensing (DCS) (Baron et al., 2005), an empirical Bayesian strategy Simultaneous Sparse Approximation in (Wipf & Rao, 2007), and a hierarchical Bayesian model for multi-task CS (Ji et al., 2007a).”
Multitask Compressive Sensing (2009, background): “The is a nuisance parameter, which in effect may have an identifiability issue [17], and an inappropriate value of it may contaminate algorithm performance significantly.”
Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference (2011, methodology): “In the MMV case, the joint sparsity among different (uncorrelated) snapshots is utilized by assuming the same sparse prior for the signals at all snapshots [12].”
Learning with structured sparsity (2009, methodology): “In order to improve forward greedy procedures, backward greedy strategies can be employed, as shown in various recent works such as Zhang (2011). For simplicity, we will not analyze such strategies in this paper.”
Compressed Sensing for Wireless Communications: Useful Tips and Tricks (2015, methodology): “For example, in SBL, it is assumed that each element of s is a zero mean Gaussian random variable with variance γ k (i.e., s k ∼ N (0 , γ k )).”
Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning (2011, methodology): “The prior for x is given by p ( x ; γ i , B i , ∀ i ) ∼ N x ( 0 , Σ 0 ) , where Σ 0 is Using the Bayes rule we obtain the posterior density of x , which is also Gaussian, with the mean and the covariance matrix So given all the hyperparameters λ, γ i , B i , ∀ i , the MAP estimate of x is given by:…”
Multibeam for Joint Communication and Radar Sensing Using Steerable Analog Antenna Arrays (2018, methodology): “We use BCS algorithm to solve the MMV problem.”
Distributed Compressive Sensing: A Deep Learning Approach (2015, methodology): “The selection of one of the above methods depends on the requirements imposed by the speciﬁc application.”
Sparse Bayesian Methods for Low-Rank Matrix Estimation (2011, background): “This is also in agreement with the original formulation of sparse Bayesian learning in [34], [40].”
Compressive Sensing in Electromagnetics - A Review (2015, methodology): “The arising evidence maximization problem has then been solved through an ad-hoc BCS strategy called temporal multiresponse sparse Bayesian learning (T-MSBL) and derived from the empirical Bayesian technique in [65].”