Since my previous work focused on ICA with applications to ECG, I have strong interests in the compressed sensing applied to ECG telemonitoring via wireless body-area networks. This is a promising application of compressed sensing because the ECG signal is "believed" sparse and compressed sensing can save much power. Thus, I read dozens of papers on this emerging application. But I'd to say, I am totally confused by current works on this direction. My main confusion is that there is few work seriously considering the noise.
You may ask: where is the noise? Let's see the basic compressed sensing model:
y = A x + v.
Of course, providing the sensor devices have high quality, the noise vector v can be very small. However, the signal x (i.e. the recorded ECG signal before compression) has strong noise!!! Note that the application is telemonitoring via wireless body-area networks. Simply put, a device (run by battery) is put on your body to record various physiological data and then send these data (via blue-tooth) to your cell-phone, iphone, ipad, ect for advanced processing, and then these data are further sent to remote terminals for other use. In this application, you are free to walk around. Your each movement, even a very small movement, may result in large disturbance and noise in the recorded signal.
To get a basic feeling about this, I paste an ECG signal recorded from a pregnant women's abdomen, who quietly lies on a bed (not walks). So the major noise comes from her breathe. (I know generally ECG sensors are put on chest. This example is just to show the noise amplitude and how it changes the sparsity of the signal.) Let's see the raw ECG data:
Can you see the noise from her breathe? Is the signal sparse or compressible? You may use some threshold to remove the noise, but you can lost some important components of the ECG signal (e.g. P wave, T wave, etc). Also, the threshold should be data-adaptive. Since different people have ECG with different amplitudes, and the contact quality of sensor to skin also affects the signal amplitude, you need some algorithms to adaptively choose a suitable threshold. And the threshold algorithm also can increase the complexity of chip design and power consuming, which make this application of compressed sensing impossible. Note that the women was quietly lying on the bed. In the real application of body-area networks, the noise from arm movement, walk, or even run is extremely larger than this.
So, I strongly suggest that future work in this topic should seriously consider the noise from movement, and should derive "super" compressed sensing algorithms for this application. And the use of the MIT-BIH dataset (has been used in many existing papers) is thus not suitable. In one of my papers in preparation, I tried many famous algorithms and all of them failed. A main reason is the field of compressed sensing is lack of algorithms considering the noise from signal itself.