Block-SBL for Recovery of Block/Group Sparse Signals

Updated: July 30, 2012

1. Introduction
The Block Sparse Bayesian Learning (BSBL) framework 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/group 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) wireless telemonitoring of physiological signals;
(2) audio and image compression;
(3) pattern recognition; 
(4) DOA estimation, etc;

There are three algorithms derived from this framework, i.e., BSBL-EM, BSBL-BO, and BSBL-L1 [1]. Among them, BSBL-EM generally has the best performance, but is the slowest.
BSBL-BO is the one with balanced performance and speed. BSBL-L1 is the fastest but its performance is slightly inferior to other two sometimes. 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, IEEE Transactions on Signal Processing, vol.61, no.8, pp.2009-2015, 2013

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

Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG via Block Sparse Bayesian Learning, IEEE Trans. Biomedical Engineering, vol.60, no.2, pp.300-309, 2013

[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
, vol.60, no.1, pp.221-224, 2013

[5] Benyuan Liu, Zhilin Zhang, Gary Xu, Hongqi Fan, Qiang Fu, Energy-Efficient Telemonitoring of Physiological Signals via Compressed Sensing: A Fast Algorithm and Power Consumption EvaluationBiomedical Signal Processing and Control, vol.11, pp.80-88, 2014

[6] Taiyong Li, Zhilin Zhang, Robust Face Recognition via Block Sparse Bayesian LearningMathematical Problems in Engineering, Volume 2013 (2013), Article ID 695976

2. Download Link:
           (or you can download it at the bottom of this page)
Current version: 1.3.4
Updated: Sep 25, 2012
    The package includes the codes of BSBL-EM, BSBL-BO and EBSBL-BO. It also includes demo files to show how to use BSBL-BO to compress/recover (non-sparse) fetal ECG signal and EEG.
    Although current codes were written for real-valued sparse signal recovery problems, they can be also used for complex-valued problems by rewriting the original problem as a real-valued problem, as shown in the note.
    In the future, I will modify the codes such that they can be directly used for complex-valued problems.

3. Highlights of the Work:

1. These algorithms have much better performance than most existing algorithms, especially for block/group sparse signals with known block partition

Below is the phase transition of BSBL algorithms in a canonical block sparse recovery experiment (N=1000); see the paper [1] for details:

Below is a comparison among well-known algorithms when block partition is given (signal length was fixed while we changed the measurement number; see the paper [1] 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 [1] for details)

2.Currently 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 telemonitoring demos in the software package

3. They may be the first algorithms that adaptively exploit intra-block correlation (not necessarily smooth signals)
. We revealed that intra-block correlation, if exploited, can significantly improve recovery performance.

Here is an experiment result showing our algorithms have better performance when intra-block correlation increases (see the paper [1] for details)

We also found that the effect of intra-block correlation to algorithm performance is different to the effect of temporal correlation in the MMV model (for temporal correlation on the algorithm performance, see

Zhilin Zhang,
Sep 25, 2012, 1:45 AM