Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

A group sparsity penalized CSI in the wavelet domain is proposed to alleviate ill-posedness within framework of a contrast-source inversion (CSI) method. It then applied retrieval large inhomogeneous dielectric scatterer from time-harmonic single-frequency data. As dependency exists between coefficients at different scales, referred as parent-child relationship, it enables yield quad tree structure. Therefore, can be regarded not only pixel-wise sparse, but also group-wise sparse. Focus put on using dual-tree complex transform ( $\mathbb {C}$ WT) properly achieve sought-after sparse representation spatial distribution contrast. provides notation="LaTeX">$\ell _{2,1}$ norm which added standard cost functional enforce onto spatially-varying The replication strategy combined with proximal method order solve overlapping problem. Simulations synthetic data configurations particular signal-to-noise ratios illustrate pros and cons approach shown overcome demanding situations. Comparisons discrete (DWT) usually performed _{1}$ confirm advantage methodology.