Abstract
The Restricted Isometry Property (RIP) is a useful measure of which measurement matrices will work for sparse recovery. The RIP-1 is an L1 variant of the RIP that can be satisfied by sparse matrices, allowing for faster embedding and recovery. While L1 minimization is guaranteed to work for all matrices satisfying the RIP-1, faster iterative techniques were only known to work when the matrix is the adjacency of an expander graph. We show that Sequential Sparse Matching Pursuit (SSMP) works on all matrices satisfying the RIP-1, giving the first demonstration of near-linear recovery time for arbitrary RIP-1 matrices.
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