Accurate Recovery of Sparse Objects With Perfect Mask Based on Joint Sparse Reconstruction

Abstract

Accurate inversion of high-contrast objects is of great interest to many researchers. In this paper, we reconstruct sparse high-contrast targets perfectly based on the joint sparse reconstruction and the contrast source inversion (CSI). First, the targets number is estimated accurately with the minimum description length (MDL) criterion. Second, with the exact targets number as a priori information, the supports of the targets are perfectly recovered based on the joint-sparse structure of the contrast sources under a multiple measurement vector (MMV) scheme. Finally, the contrast is perfectly reconstructed with the CSI method, in which a priori information about the accurate supports is added. The perfect mask is such strong a priori information that the reconstruction is enforced to locate on the positions of real targets, enormously enhancing the rebuilding quality. Perfect reconstructions of sparse objects with high contrast are demonstrated under various scenarios, showing effectiveness and robustness of the proposed method. Moreover, limitations of the proposed method are discussed, which explains the difference of success rate of accurate reconstruction with different mesh sizes from a physical insight. INDEX TERMS Compressive sensing, contrast source inversion (CSI), electromagnetic inverse scattering, joint sparse, perfect mask.

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