We propose a new image recovery method to improve the resolution in microwave imaging applications. Scattered field data obtained from a simplified breast model with closely located targets is used to formulate an electromagnetic inverse scattering problem, which is then solved using the Distorted Born Iterative Method (DBIM). At each iteration of the DBIM method, an underdetermined set of linear equations is solved using our proposed sparse recovery algorithm, IMATCS. Our results demonstrate the ability of the proposed method to recover small targets in cases where traditional DBIM approaches fail. Furthermore, in order to regularize the sparse recovery algorithm, we propose a novel L(2) -based approach and prove its convergence. The simulation results indicate that the L(2)-regularized method improves the robustness of the algorithm against the ill-posed conditions of the EM inverse scattering problem. Finally, we demonstrate that the regularized IMATCS-DBIM approach leads to fast, accurate and stable reconstructions of highly dense breast compositions.
Abstract-In this paper, we present a compressive sampling and Multi-Hypothesis (MH) reconstruction strategy for video sequences which has a rather simple encoder, while the decoding system is not that complex. We introduce a convex cost function that incorporates the MH technique with the sparsity constraint and the Tikhonov regularization. Consequently, we derive a new iterative algorithm based on these criteria. This algorithm surpasses its counterparts (Elasticnet and Tikhonov) in the recovery performance. Besides it is computationally much faster than the Elasticnet and comparable to the Tikhonov. Our extensive simulation results confirm these claims.
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