1. Why provided the sensing matrix Phi in the software package?

The *Phi.mat*in the software package stores a binary sparse matrix, which is used as the sensing matrix. But I have to emphasize that it is not an optimal sensing matrix. I just randomly generated it and then stored it and used it for all my experiments. This can help people exactly reproduce my results (When the dataset is given, different sensing matrices can result in slightly different performance). As you know, designing an optimal sparse sensing matrix is an important direction in compressed sensing.

2. Can the demo files for telemonitoring of fetal ECG be directly used in a telemonitoring system?

The demo files for telemonitoring of fetal ECG are just a mimicking of telemonitoring. In a real system, each channel recording should be processed by a BSBL-BO algorithm (parallel computation), and may need to use online ICA algorithms or at least on-line batch algorithms. The ICA algorithm used in the demo files is an off-line algorithm. You can use the (Extended-) Infomax algorithm, an online algorithm which can be accessed from the EEGLab.

3. Have you made any real telemonitoring systems using the algorithm?

The second author (Prof. Tzyy-Ping Jung) has led a team to build real-time telemonitoring systems for EEG, and some products have being sold in Taiwan.But these systems have not used compressed sensing technique. However, we are now considering to incorporate some BSBL algorithm. For your interests, please check the following links to see the videos on these telemonitoring systems for various applications:

http://sccn.ucsd.edu/~jung/Site/Demos.html

4. Can BSBL-BO work well when used in the in-direct recovery way (i.e. first recovering the representation coefficients of the signal in some transformed domain, and then recovering the original signal)?

Yes, of course. In the *DEMO_nonSparse.m*I also give an example when BSBL-BO first recovers the DCT coefficients and then recovers the original fetal ECG. The performance is improved in this way. But such method does not work well for all physiological signals. In my experiments on some public EEG and EMG datasets, BSBL-BO using this method may have poorer performance than not using this method.

5. Speed Improvement

I am very glad that some people are interested in the BSBL-BO and
want to try in their work. Please note the code is not optimized for
speed. I chose a coding style for readability instead of for speed.
There are some ways to improve the code:(1) Remove many "if-" in the code. The current code considers many simulation scenarios, such as block sparsity model with known partition (identical block size or random block size), with unknown partition, and recovery of non-sparse structured signals, etc. According to your problem, you can remove those unnecessary parts.

(2) There is a matrix inverse in each iteration. You can replace the current method by other fast matrix inverse method (check matrix computation textbooks), or consider the fast strategy used in Tipping and Faul (2003).

(3) The updating of the intra-block correlation value in each iteration is not necessary. In some cases, you can figure out a good value according to a priori information. Also, the updating of noise variance in each iteration is not necessary.

(4) Although I have said that BSBL-L1 is not suitable for telemonitoring of non-sparse physiological signals in the paper, later I found when replacing the group-Lasso type algorithms in the BSBL-L1 with some specific algorithms, we can get good performance with dramatically accelerated speed.

Of course, as the author of the algorithm, I am responsible for making the code more efficient. When I have time, I will improve it along these ways. But in the near future I have no time to further improve it (Currently I am now deriving SBL algorithms to solve multi-modal/multi-dataset/longitudinal problems in neuroimaging). If you have improved it, or if you want to improve it, please let me know. I would like to share my ideas with you, and collaboration is welcome.