CS: Q&As, Sensing Matrix Optimization for Block-Sparse Decoding

The Compressive Sensing Group on LinkedIn now features 578 members:. Some of the recent questions include:

• Juan asks a rather long question:CS for Stipmap SAR Radar Imaging
• Arun also asks: Can anyone tell me which algorithm works well for sparse reconstruction using complex matrices. I'm using OMP but the probability of error seems to be too large

On the CS Theory Q&A site, Suresh provided an answer to the complexity of the SL0 algorithm which sounds right. The CS Theory Q&A site has crossed the 1000 user mark. Woohoo.

On Arxiv, the following interesting paper just showed up: Sensing Matrix Optimization for Block-Sparse Decoding by: Kevin Rosenblum, Lihi Zelnik-Manor, Yonina C. Eldar. The abstract reads:

Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the atoms of the equivalent dictionary, and as a consequence, reduce the reconstruction error. In some applications, the signals of interest can be well approximated by a union of a small number of subspaces (e.g., face recognition and motion segmentation). This implies the existence of a dictionary which leads to block-sparse representations. In this work, we propose a framework for sensing matrix design that improves the ability of block-sparse approximation techniques to reconstruct and classify signals. This method is based on minimizing a weighted sum of the inter-block coherence and the sub-block coherence of the equivalent dictionary. Our experiments show that the proposed algorithm significantly improves signal recovery and classification ability of the Block-OMP algorithm compared to sensing matrix optimization methods that do not employ block structure.