Semi definite Programming for Computable Performance Bounds on Block-Sparsity Recovery - 2016
In this paper, we have a tendency to use mounted point theory and semidefinite programming to compute the performance bounds on convex block-sparsity recovery algorithms. As a requirement for optimal sensing matrix design, computable performance bounds would open doors for wide applications in sensor arrays, radar, DNA microarrays, and several other areas where block-sparsity arises naturally. We have a tendency to outline a family of quality measures for arbitrary sensing matrices as the optimal values of sure optimization issues. The reconstruction errors of convex recovery algorithms are bounded in terms of these quality measures. We demonstrate that as long as the amount of measurements is comparatively large, these quality measures are bounded faraway from zero for a giant class of random sensing matrices, a result parallel to the probabilistic analysis of the block restricted isometry property. As the primary contribution of this work, we associate the quality measures with the mounted points of functions defined by a series of semidefinite programs. This relation with fastened purpose theory yields polynomial-time algorithms with world convergence guarantees to compute the standard measures.
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