Compressive Sensing for Tomographic Imaging of a Target with a Narrowband Bistatic Radar

Abstract

This paper introduces a new approach to bistatic radar tomographic imaging based on the concept of compressive sensing and sparse reconstruction. The field of compressive sensing has established a mathematical framework which guarantees sparse solutions for under-determined linear inverse problems. In this paper, we present a new formulation for the bistatic radar tomography problem based on sparse inversion, moving away from the conventional k-space tomography approach. The proposed sparse inversion approach allows high-quality images of the target to be obtained from limited narrowband radar data. In particular, we exploit the use of the parameter-refined orthogonal matching pursuit (PROMP) algorithm to obtain a sparse solution for the sparse-based tomography formulation. A key important feature of the PROMP algorithm is that it is capable of tackling the dictionary mismatch problem arising from off-grid scatterers by perturbing the dictionary atoms and allowing them to go off the grid. Performance evaluation studies involving both simulated and real data are presented to demonstrate the performance advantage of the proposed sparsity-based tomography method over the conventional k-space tomography method.

Direct 3-D Sparse Imaging Using Non-Uniform Samples Without Data Interpolation

“…Although full 3-D imaging is an advisable way, using Fourier processing methods, such as 3-D non-uniform fast Fourier transform (3-D NUFFT), generates poor imaging results with high side-lobes due to the sparsity of the k-space samples [17,18]. Sparse reconstruction is a method of model matching, in which regularization enforcing sparsity to obtain sparse results [19,20]. Combining the sparse reconstruction with the sparsity of the data to carry out 3-D sparse imaging for non-uniform samples is expected to reduce high side-lobes and obtain high-resolution imaging results.…”