Microwave Imaging of Nonsparse Object Using Dual-Mesh Method and Iterative Method with Adaptive Thresholding

A new microwave image reconstruction method is proposed to recover a nonsparse object using the iterative method with adaptive thresholding for compressed sensing (IMATCS) method. First, a dual-mesh method discretizes the object using the Distmesh generator tool, which automatically generates size functions and adapts to the curvature and the feature size of the geometry. Near field scattered data collected from a circular phantom are used to solve the inverse scattering problem using the distorted Born iterative method (DBIM). At every iteration during DBIM, the forward problem is formulated as an underdetermined set of linear equations. Then, the IMATCS method is applied to solve the linear equations. IMATCS is a L₂-regularized approach to solve the sparse recovery problem, which improves the robustness of the algorithm. Next, the nondecimated wavelet transform (NDWT) method is applied to transform the nonsparse signal into a sparse signal which acts as an input to the IMATCS process. As a result, the new proposed NDWT based on IMATCS method (NDW-IMATCS) is able to recover the nonsparse signal and leads to the reconstruction results. Finally, we demonstrate that our dual-mesh method combined with the NDW-IMATCS algorithm leads to fast, accurate, and stable reconstructions of nonsparse objects.