In this paper, the Compressive Sampling Matching Pursuit Algorithm (CoSaMP) is applied to microwave reconstruction of a 2-dimensional non-sparse object. First, an adaptive discretization method, DistMesh method, is applied to discretize the image domain based on the region of interest. The dual-mesh method is able to provide denser and smaller discretized cells in more important areas of the object and larger cells in other areas, thereby providing more details in the interest domain and keeping the computational burden at a reasonable level. Another benefit of using the dual-mesh method is that it automatically generates size functions and adapts to the curvature and the feature size of the geometry. In addition, the size of each cell changes gradually. Next, the inverse scattering problem is solved in frame of Distorted Born Iterative Method (DBIM). During each iteration of DBIM, the near field scattering problem is modeled as a set of linear equations. Furthermore, a compressive sensing (CS) method called the Compressive Sampling Matching Pursuit Algorithm is applied to solve the nonlinear inverse problem. During this process, two innovative steps are applied. First, for the reconstruction of the non-sparse object, the signal input to our algorithm is processed via a wavelet transformation to obtain sparsity. Second, as the dual-mesh method discretizes more important cells in smaller sizes, these cells have high potential to be filtered by the threshold of CoSaMP. As a result, a regularization matrix is introduced to reduce the effect of size. Finally, we present numerical experiment results based on our dual-mesh method combined with the regularized CoSaMP algorithm.
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