**Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Non-Invasive Fetal ECG via Block Sparse Bayesian Learning,**

by Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao, accepted by IEEE Trans. Biomedical Engineering.

Available at:

**http://arxiv.org/abs/1205.1287**, Codes can be downloaded at:

**http://dsp.ucsd.edu/~zhilin/BSBL.html**, or

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

Note that there are two groups of works on compressed sensing of ECG.

**One is the ECG compression (just like video compression, image compression, etc)**. Most works actually belong to this group. They generally use some MIT-BIH datasets, which are very clean (noise is removed).

**Another group is compressed sensing of ECG for energy-efficient wireless telemonitoring**. There are only few works in this group. Our work belongs to this group. In this group

**the ECG data is always contaminated by noise and artifacts ('signal noise').**This is because the goal of telemonitoring is to allow people to walk and even exercise freely, and thus

**strong noise and artifacts caused by muscle and electrode movement are inevitable**. Furthermore,

**artifacts caused by battery power level also cannot be ignored**. Consequently, the raw ECG recordings are not sparse in the time domain and also not sparse in the transformed domains (e.g. the wavelet domain, the DCT domain). However, the strict constraint on energy consumption (and design issues, etc) of telemonitoring systems does not encourage filtering or other preprocessing before compression. Or, put in another way, if energy consumption and design issues are not problems, CS may have no advantages over traditional methods. Thus, CS algorithms have to recover non-sparse signals for this application. It turns out that the problem is very challenging.

**Our work not only solves this challenging problem, but also has some interesting mathematical meanings:**

**By linear algebra, there are infinite solutions to the underdetermined problem y=Ax. When the true solution x0 is sparse, using CS algorithms it is possible to find it. But when the true solution x0 is non-sparse, finding it is more challenging and new constraints/assumptions are called for. This work shows that when exploiting the unknown block structure and the intra-block correlation of x0, it is possible to find a solution x_est which is very close to the true solution x0. These findings raise new and interesting possibilities for signal compression as well as theoretical questions in the subject of sparse and non-sparse signal recovery from a small number of measurements y.**

**Below is the paper's Abstract:**

Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body-area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as non-sparsity and strong noise contamination, current CS algorithms generally fail in this application.

This work proposes to use the block sparse Bayesian learning (BSBL) framework to compress/reconstruct non-sparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.

PS: When I wrote this paper, I was in my wife's delivery room. My wife was lying on the bed, resting and waiting for her midwife. I was sitting beside her, writing the paper in my laptop (and trying to finish the main framework before the miracle moment). Now the baby is 8-month.

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