Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning

By Zhilin Zhang, Bhaskar D. Rao. IEEE Journal on Selected Topics in Signal Processing, 2011

825 citations recorded by the source corpus.

We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal correlation and thus their performance degrades significantly with the correlation. In this paper, we propose a block sparse Bayesian learning framework which models the temporal correlation. We derive two sparse Bayesian learning (SBL) algorithms, which have superior recovery performance compared to existing algorithms, especially in the presence of high temporal correlation. Furthermore, our algorithms are better at handling highly underdetermined problems and require less row-sparsity on the solution matrix. We also provide analysis of the global and local minima of their cost function, and show that the SBL cost function has the very desirable property that the global minimum is at the sparsest solution to the MMV problem. Extensive experiments also provide some interesting results that motivate future theoretical research on the MMV model.

Subfields: Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/b104e4db9e9f431b19eb8cfd8bb1f4cab1c742bc

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Citations in the corpus

Compressive Sensing in Electromagnetics - A Review (2015, methodology): “Furthermore, temporal correlation between successive CS inversion processes has been also considered, by introducing a block-sparse Bayesian framework [48].”
Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG Via Block Sparse Bayesian Learning (2012, methodology): “It provides large flexibility to exploit spatial [14], temporal [15], and dynamic structure [16] of signals.”
Distributed Compressive Sensing: A Deep Learning Approach (2015, background): “The selection of one of the above methods depends on the requirements imposed by the speciﬁc application.”
Multibeam for Joint Communication and Radar Sensing Using Steerable Analog Antenna Arrays (2018, methodology): “For each R(nt), we can then apply some MMV CS algorithm such as MMV Bayesian Compressive Sensing (BCS) [23], [24] or MMV OMP [25] to get estimates for U.”
Expectation-Maximization Gaussian-Mixture Approximate Message Passing (2012, methodology): “For comparison, we show the performance of the proposed EM-GM-GAMP (in “sparse” mode), EM-BG-GAMP [12], Bayesian Compressive Sensing (BCS) [11], Sparse Bayesian Learning [10] (via T-MSBL [15]), debiased genie-aided 8 Lasso (via SPGL1 [16]), and Smoothedl0 (SL0) [17].”
Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference (2011, methodology): “1The correlations between columns of the signal matrix ( in our case) have recently been studied in [13].”
Iterative Channel Estimation Using LSE and Sparse Message Passing for MmWave MIMO Systems (2016, methodology): “5 shows the average channel estimation NMSE performance of the proposed LSE-SMP algorithm, LSE, Genie aided ITD-SE [27], genie-tuned LASSO (via SPGL1 [75]), SBL [30] (via the T-MSBL [31]), genie-tuned OMP [29], EM-BG-AMP [33] (in sparse mode) and BP-MF SBL [34].”
Compressed Sensing for Wireless Communications: Useful Tips and Tricks (2015, methodology): “TSBL [85] Equivalence between block sparsity model and MMV model was used to exploit the correlations between the source vectors.”
Photoplethysmography-Based Heart Rate Monitoring in Physical Activities via Joint Sparse Spectrum Reconstruction (2015, methodology): “Using the MMV model has many benefits, which cannot be obtained when using the SMV model: 1) Based on theoretical analysis, given the same sparsity level and compression ratio, the MMV model is known to have much better reconstruction performance than the SMV model [13]–[15].”
Sparse Bayesian multi-task learning for predicting cognitive outcomes from neuroimaging measures in Alzheimer's disease (2012, methodology): “Using (18) and following the simplification procedure in [26] we obtain the simplified algorithm as follows:”
Extension of SBL Algorithms for the Recovery of Block Sparse Signals With Intra-Block Correlation (2012, methodology): “We find the effect of intra-block correlation is quite different from the effect of temporal correlation in an MMV model [11].”