Friday, September 10, 2010

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:
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.

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