Divide and conquer method for sparsity estimation within compressed sensing framework

A novel method for sparsity estimation by means of the divide and conquer method is presented. Also, the underestimation and overestimation criteria for signal sparsity is proposed and proven. Then the blind-sparsity subspace pursuit (BSP) algorithm for sparse reconstruction is discussed. Based on the estimation, BSP combines the support set and inherits the backtracking refinement that attaches to compressive sampling matching pursuit (CoSaMP)/subspace pursuit (SP), whereas the pruning process of BSP is improved by introducing the weakly matching backtracking strategy. With the said improvement, there is no need for BSP to require the sparsity as an input parameter. Furthermore, experiments demonstrate that the divide and conquer method is effective for sparsity estimation when the isometry constant is known. In addition, the simulation results also validate the superior performance of the new algorithm and show that BSP is an excellent algorithm for blind sparse reconstruction and is robust when the estimate of sparsity is not perfectly accurate.