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BSBL for Recovery of Block Sparse Signal with Known or Unknown Block Partition

University of California, San Diego

Updated: Sep 25, 2012

Latest updates can be found at:

https://sites.google.com/site/researchbyzhang/bsbl

1.Introduction

BSBL is a block Sparse Bayesian Learning framework, which explores and exploits the intra-block correlation (i.e. correlation of values of entries within each block) in the block sparse model. Algorithms derived from this model can successfully solve the following sparse signal recovery/compressed sensing problems with superior performance to most existing algorithms:

(1) recovery of block sparse signals with block partition (the partition can be known or unknown) [1,2]

(2) recovery of non-sparse signals with or without any structure (not necessarily is the block structure) [3,4]

Up to now BSBL has successfully solved many difficult problems in a number of applications, such as:

(1) telemonitoring of non-sparse physiological signals via wireless body-area networks [3,4];

(2) audio and image compression;

(3) pattern recognition;

There are three algorithms derived from this framework. They are BSBL-EM, BSBL-BO, and BSBL-L1 [1]. BSBL-EM has the best performance, but is lowest. BSBL-L1 is the fastest but its performance is not good as other two in general cases. BSBL-BO is the one with balanced performance and speed. Besides, BSBL-L1 provides strategies to improve existing algorithms such as group Lasso so that they can also effectively exploit intra-block correlation.

Below are related papers:

[1] Zhilin Zhang, Bhaskar D. Rao, Extension of SBL Algorithms for the Recovery of Block Sparse Signals with Intra-Block Correlation, to appear in IEEE Transaction on Signal Processing

[2] Zhilin Zhang, Bhaskar D. Rao, Recovery of Block Sparse Signals Using the Framework of Block Sparse Bayesian Learning, ICASSP 2012

[3] Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Non-Invasive Fetal ECG via Block Sparse Bayesian Learning, IEEE Trans. Biomedical Engineering, accepted

[4] Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, Compressed Sensing of EEG for Wireless Telemonitoring with Low Energy Consumption and Inexpensive Hardware, IEEE Trans. Biomedical Engineering, accepted

2.Download Link

Link: dsp.ucsd.edu/~zhilin/BSBL_public.zip
Current version: 1.3.4
Updated: Sep 25, 2012
Remarks: The package includes the codes of BSBL-EM, BSBL-BO and EBSBL-BO. It also includes some demo files to perform experiments when block partition is known and unknown. Besides, there are demo files to show how to use BSBL-BO to compress/recover non-sparse fetal ECG signal and EEG in telemonitoring sceanrios.

(Latest updates can be found at: https://sites.google.com/site/researchbyzhang/bsbl. Or, send email to me)

3.Highlights of bSBL

(1) These algorithms may have the best recovery performance among existing algorithms (to our best knowledge)

Here is a comparison among all well-known algorithms when block partition is given (signal length was fixed while we changed the measurement number; see the paper for details)

Here is a comparison among existing algorithms when block partition is unknown (signal length, measurement number, and the number of nonzero elements in the signal were fixed while we changed the nonzero block number; each block had random size and location. See the paper for details)

(2)They are the only algorithms that can recover non-sparse signals with unknown structure and do not necessarily need to transform the signals to other domains (e.g. wavelet domains).

Here is a result using BSBL-BO to recover a non-sparse signal with unknown structure, while using a simple sparse binary sensing matrix (175 x 384). To our knowledge, no other algorithms can do this with such recovery quality by using this type of sensing matrices (these sensing matrices are required in telemonitoring for ultra-low energy consumption). See the paper [3,4] for details; and run the demo file DEMO_nonSparse.m and the demo files in two sub-folds in the above software package.

(3)They may be the first algorithms that adaptively exploit intra-block correlation, i.e. the correlation among elements of a block.

(4)We revealed that intra-block correlation, if exploited, can significantly improve recovery performance and reduce the number of measurements.

Here is an experiment result showing our algorithms have better performance when intra-block correlation increases (see the paper for details)

But we also found that the intra-block correlation has little effects on the performance of existing algorithms. This is different to our finding on the MMV model, where we found temporal correlation has obvious negative effects on the performance of existing algorithms (for temporal correlation on the algorithm performance, see here).

Here is an experiment result showing the performance of Block-CoSaMP and Block-OMP is almost not affected by the intra-block correlation (see the paper for details).