Multiple pattern classification by sparse subspace decomposition

A robust classification method is developed on the basis of sparse subspace decomposition. This method tries to decompose a mixture of subspaces of unlabeled data (queries) into class subspaces as few as possible. Each query is classified into the class whose subspace significantly contributes to the decomposed subspace. Multiple queries from different classes can be simultaneously classified into their respective classes. A practical greedy algorithm of the sparse subspace decomposition is designed for the classification. The present method achieves high recognition rate and robust performance exploiting joint sparsity.Comment: 8 pages, 3 figures, 2nd IEEE International Workshop on Subspace Methods, Workshop Proceedings of ICCV 200

Joint Block-Sparse Recovery Using Simultaneous BOMP/BOLS

We consider the greedy algorithms for the joint recovery of high-dimensional sparse signals based on the block multiple measurement vector (BMMV) model in compressed sensing (CS). To this end, we first put forth two versions of simultaneous block orthogonal least squares (S-BOLS) as the baseline for the OLS framework. Their cornerstone is to sequentially check and select the support block to minimize the residual power. Then, parallel performance analysis for the existing simultaneous block orthogonal matching pursuit (S-BOMP) and the two proposed S-BOLS algorithms is developed. It indicates that under the conditions based on the mutual incoherence property (MIP) and the decaying magnitude structure of the nonzero blocks of the signal, the algorithms select all the significant blocks before possibly choosing incorrect ones. In addition, we further consider the problem of sufficient data volume for reliable recovery, and provide its MIP-based bounds in closed-form. These results together highlight the key role of the block characteristic in addressing the weak-sparse issue, i.e., the scenario where the overall sparsity is too large. The derived theoretical results are also universally valid for conventional block-greedy algorithms and non-block algorithms by setting the number of measurement vectors and the block length to 1, respectively.Comment: This work has been submitted to the IEEE for possible publicatio

Compressed Sensing and Parallel Acquisition

Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating such problems by providing more overall measurements. In this work we consider the combination of compressed sensing with parallel acquisition. We establish the theoretical improvements of such systems by providing recovery guarantees for which, subject to appropriate conditions, the number of measurements required per sensor decreases linearly with the total number of sensors. Throughout, we consider two different sampling scenarios -- distinct (corresponding to independent sampling in each sensor) and identical (corresponding to dependent sampling between sensors) -- and a general mathematical framework that allows for a wide range of sensing matrices (e.g., subgaussian random matrices, subsampled isometries, random convolutions and random Toeplitz matrices). We also consider not just the standard sparse signal model, but also the so-called sparse in levels signal model. This model includes both sparse and distributed signals and clustered sparse signals. As our results show, optimal recovery guarantees for both distinct and identical sampling are possible under much broader conditions on the so-called sensor profile matrices (which characterize environmental conditions between a source and the sensors) for the sparse in levels model than for the sparse model. To verify our recovery guarantees we provide numerical results showing phase transitions for a number of different multi-sensor environments.Comment: 43 pages, 4 figure