BSBL-FM

This is a fast implementation of the Block Sparse Bayesian Learning BSBL algorithm. The developed algorith is based on the Fast Marginalized (FM) likelihood maximization algorithm, which yields ~8 times speedup while also pertains nearly the same recovery performances.

A Python version of BSBL algorithms is also available: pyBSBL

A Short Introduction

A CS algorithm aims to solve, Y = Phi X + N, where Y is the measurement matrix of size M times T, Phi is the under-determined sensing matrix of size M times N, X is the signal.

Compressed sensing, can recover X given Y and the under-determined matrix Phi. When T=1, we called it Single Measurement Vector (SMV) Model, with T>1, it is the Multiple Measurement Vector (MMV) model.

Block Sparse, assumes that x can be partitioned into blocks x = {x_1, ... , x_g}. The non-zero entries cluster within some blocks and zeros otherwise. If d out of g blocks are non-zero, then the block sparsity is defined as d/g. Exploiting both the block sparsity and the intra-block correlation is the source of the magic of all BSBL algorithms.

Our BSBL-FM algorithm, is an ultra fast implementation of the original BSBL framework, which brings about ~8 times speedup. What's more, It can worked in all the scenarios include:

• SMV sparse
• MMV sparse
• SMV block sparse
• MMV block sparse
• Real-valued
• Complex-valued

See the demos and implementations below for more details.

Codes and Data

The .m codes are:

CODE:

• BSBL_FM.m: the main algorithm, also called MBSBL-FM in MMV model
• BSBL_BO.m: Zhilin's BSBL-BO algorithm.
• demo_smv_real.m: the real valued SMV block sparse demo
• demo_smv_complex.m: the complexed valued SMV block sparse demo
• demo_mmv.m: the real valued MMV block sparse demo
• demo_fecg.m: the demo code for FECG dataset recovery

The .mat data files are:

DATA:

• demo.mat: the data for SMV case, contains re, im vectors
• signal_01.mat: FECG datasets used in BSBL-BO by Zhilin
• Phi.mat: the sensing matrix for CS FECG data

Citations

If you find the BSBL-FM algorithm useful, please cite:

@Article{liu2013energy,
    Title = {Energy Efficient Telemonitoring of Physiological Signals via Compressed Sensing: A Fast Algorithm and Power 
Consumption Evaluation},
    Author = {Liu, Benyuan and Zhang, Zhilin and Xu, Gary and Fan, Hongqi and Fu, Qiang},
    Journal = {Biomedical Signal Processing and Control},
    Year = {2014},
    Pages = {80--88},
    Volume = {11C}
}

@InProceedings{liu2013compression,
    Title = {Compression via Compressive Sensing: A Low-Power Framework for the Telemonitoring of Multi-Channel Physiological 
Signals},
    Author = {Benyuan Liu and Zhilin Zhang and Hongqi Fan and Qiang Fu},
    Booktitle = {2013 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)},
    Year = {2013},
    Organization = {IEEE},
    Pages = {9--12}
}

More powerful STSBL algorithm developed by Zhilin Zhang is available on-line:

@InProceedings{ZhangAsilomar2013,
    Title = {Compressed Sensing for Energy-Efficient Wireless Telemonitoring: Challenges and Opportunities},
    Author = {Zhilin Zhang and Bhaskar D. Rao and Tzyy-Ping Jung},
    Booktitle = {Asilomar Conference on Signals, Systems, and Computers (Asilomar 2013)},
    Year = {2013}
}

@Article{zhang2014spatiotemporal,
    Title = {Spatiotemporal Sparse Bayesian Learning with Applications to Compressed Sensing of Multichannel EEG for Wireless 
Telemonitoring and Brain-Computer Interfaces},
    Author = {Zhilin Zhang and Tzyy-Ping Jung and Scott Makeig and Bhaskar D. Rao and Zhouyue Pi},
    Journal = {(Accepted) IEEE Trans. on Neural Systems and Rehabilitation Engineering},
    Year = {2014}
}