Bayesian Compressive Sensing

By Shihao Ji, Ya Xue, Lawrence Carin. IEEE Transactions on Signal Processing, 2008

2,366 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Networks and Communications, Signal Processing

View Paper: https://www.semanticscholar.org/paper/20287d3e224fea314ecb855238ece6677c216a1b

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In Computational Mechanics

In Computer Networks and Communications

In Signal Processing

Citations in the corpus

Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing (2009, methodology): “The structure associated with typical wavelet coefficients has been utilized in a statistical setting, building on recent research on Bayesian CS [15].”
Structured Compressed Sensing: From Theory to Applications (2011, neutral): “Approaches designed to address stochastic noise include complexity-based regularization [52] and Bayesian estimation [53].”
Bayesian Compressive Sampling for Pattern Synthesis With Maximally Sparse Non-Uniform Linear Arrays (2011, methodology): “Towards this end, an efficient solver exploiting a fast relevance vector machine algorithm [32], [36] is adopted.”
Compressed Sensing using Generative Models (2017, background): “, 2017) that connects model-based compressed sensing with the invertibility of Convolutional Neural Networks, Bayesian compressed sensing (Ji et al., 2008) and compressive sensing using Gaussian mixture models (Yang et al.”
Sparse Methods for Direction-of-Arrival Estimation (2016, background): “The first class is within the framework of SBL (see, e.g., [119–122]).”
Multi-task compressive sensing with Dirichlet process priors (2008, methodology): “One advantage of BCS is that this framework may be extended to multi-task compressive sensing (Ji et al., 2007a), in which each CS measurement vi = <i .i represents a sensing task and the objective is to jointly invert for all {.i}i=1,M , through an appropriate sharing of information between the…”
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images (2011, background): “In most applications of CS, is assumed known, corresponding to an orthonormal basis (e.g., wavelets or a DCT) [5], [9], [21].”
Microwave Imaging Within the First-Order Born Approximation by Means of the Contrast-Field Bayesian Compressive Sensing (2012, methodology): “, variance) of around its mean value must be evaluated [49].”
A unified Bayesian framework for MEG/EEG source imaging (2009, neutral): “…of g i ( • ) defined via the duality relationship g 4 i a ð Þ ¼ min zz0 az À g i z ð Þ ½ : ð34Þ For what follows, it is not crucial that these expressions be fully digested; however, Jordan et al. (1999) contains a very accessible treatment of conjugate duality and related concepts that are…”
Kalman filtered Compressed Sensing (2008, background): “If at a given time, there is an addition to the support set, but we run the KF for the old model, there will be a model mismatch and the innovation (andfiltering) error will increase.”
Expectation-Maximization Gaussian-Mixture Approximate Message Passing (2012, positive): “Compared with previously proposed empirical-Bayesian approaches to compressive sensing (e.g., [17]–[19]), ourshas a more flexible signal model, and thus is able to better match a wide range of signal pdfspX(·), as we demonstrate through a detailed numerical study.”
Robust sparse coding for face recognition (2011, methodology): “The Bayesian methods were also used for designing the sparsity regularization terms [11].”
Multitask Compressive Sensing (2009, methodology): “In the context of a regression analysis, we assume [10]”
Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices (2012, background): “A number of works also adopted a probabilistic or Bayesian approach [20]–[22].”