  We present a compressive sensing based defect detection by multiple input
multiple output (MIMO) wireless radar. Here, defects are inside a layered
material structure, therefore, due to reflections from the surface of the
layered material structure the defect detection is challenging. By utilizing a
low-rank nature of the reflections of the layered material structure and sparse
nature of the defects, we propose a method based on rank minimization and
sparse recovery. To improve the accuracy in the recovery of low-rank and sparse
components, we propose a non-convex approach based on the iteratively
reweighted nuclear norm and iteratively reweighted $\ell_1-$norm algorithm. Our
numerical results show that the proposed method is able to demix and recover
the signalling responses of the defects and layered structure successfully from
substantially reduced number of observations. Further, the proposed approach
outperforms the state-of-the-art clutter reduction approaches
