Exploiting Correlation in Sparse Signal Recovery Problems: Multiple Measurement Vectors, Block Sparsity, and Time-Varying Sparsity

A trend in compressed sensing (CS) is to exploit structure for improved reconstruction performance. In the basic CS model (i.e. the single measurement vector model), exploiting the clustering structure among nonzero elements in the solution vector has drawn much attention, and many algorithms have been proposed such as group Lasso (Yuan & Lin, 2006). However, few algorithms explicitly consider correlation within a cluster. Meanwhile, in the multiple measurement vector (MMV) model (Cotter et al., 2005) correlation among multiple solution vectors is largely ignored. Although several recently developed algorithms consider the exploitation of the correlation, such as the Kalman Filtered Compressed Sensing (KFCS) (Vaswani, 2008), these algorithms need to know a priori the correlation structure, thus limiting their effectiveness in practical problems.