Robust Sparse Signal Recovery for Compressed Sensing with Sampling and Representation Uncertainties - implementation -

Yipeng Liu just sent me the following

Dear Igor,

....We propose one method that is more robust to multiplicative uncertainty when recovering sparse signal from compressive measurements. I guess it may be interesting to some of your nuit blanche blog reader. It is online available at: ftp://ftp.esat.kuleuven.ac.be/pub/SISTA//yliu/rl0.pdf

Thank you very much for the daily updating posting! Your blog really help me a lot!
Best Regards, 
2013-10-23

Yipeng Liu （刘翼鹏）, PhD, Research Fellow
ESAT-STADIUS, Department of Electrical Engineering, University of Leuven
Email: yipeng.liu@esat.kuleuven.be; dr.yipengliu@gmail.com
Kasteelpark Arenberg 10, box 2446, 3001 Heverlee, Belgium

Here is the report:

``Robust Sparse Signal Recovery for Compressed Sensing with Sampling and Representation Uncertainties'', Yipeng Liu, Maarten De Vos. Sabine Van Huffel, Internal Report 12-177, ESAT-SISTA, K.U.Leuven (Leuven, Belgium), 2012.

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and dictionary are assumed be known exactly in advance. However, uncertainties exist due to sampling distortion, finite grids of the parameter space of dictionary, etc. In this paper, we take a generalized sparse signal model, which simultaneously considers the sampling and dictionary uncertainties. Based on the new signal model, a new optimization model for robust sparse signal recovery is proposed. This optimization model can be deduced with stochastic robust approximation analysis. Both convex relaxation and greedy algorithm are used to solve the optimization problem. For the convex relaxation method, a sufficient condition for recovery by convex relaxation method and the uniqueness of solution are given too; For the greedy sparse algorithms, it is realized by the introduction of a pre-processing of the sensing matrix and the measurements. In numerical experiments, both simulated data and real-life ECG data based results show that the proposed method has a better performance than the current methods.

The implementation is here.
"In Folder A, the codes for Fig. 3 are given. Fig. 4 and 5 can be provided by just a few parameters. In Folder B,  all the data and Figures can be generated by the codes."
Thank you Yipeng
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