Sparse Reconstruction for Near-Field MIMO Radar Imaging Using Fast Multipole Method

Emre A Miran,Sencer Koc,Figen S Oktem

doi:10.1109/access.2021.3126472

Abstract

Radar imaging using multiple input multiple output systems are becoming popular recently. These applications typically contain a sparse scene and the imaging system is challenged by the requirement of high quality real-time image reconstruction from under-sampled measurements via compressive sensing. In this paper, we deal with obtaining sparse solution to near- field radar imaging problems by developing efficient sparse reconstruction, which avoid storing and using large-scale sensing matrices. We demonstrate that the “fast multipole method” can be employed within sparse reconstruction algorithms to efficiently compute the sensing operator and its adjoint (backward) operator, hence improving the computation speed and memory usage, especially for large-scale 3-D imaging problems. For several near-field imaging scenarios including point scatterers and 2-D/3-D extended targets, the performances of sparse reconstruction algorithms are numerically tested in comparison with a classical solver. Furthermore, effectiveness of the fast multipole method and efficient reconstruction are illustrated in terms of memory requirement and processing time.

Highlights

Radar imaging has many applications such as subsurface or behind wall imaging, improvised explosive device detection, and collision avoidance and has been of interest in the literature, recently [1,2,3,4]
RECONSTRUCTION ALGORITHMS We have considered two convex optimization based algorithms for sparse reconstruction, namely, Alternating direction method of multipliers (ADMM) and CSALSA-2 and they are explained in the following subsections
NUMERICAL RESULTS Several near-field imaging problems are considered to investigate the performance of augmented Lagrangian approach and the related algorithms described above

Summary

INTRODUCTION

Radar imaging has many applications such as subsurface or behind wall imaging, improvised explosive device detection, and collision avoidance and has been of interest in the literature, recently [1,2,3,4]. Orthogonal matching pursuit (OMP) is a greedy method based on l0 “norm” It approximates a sparse solution by iteratively selecting a column of the sensing matrix, which contribute to the sparsity most. Greedy methods work under specific conditions and does not require exhaustive search Another useful approach for sparse approximation is to replace the l0 “norm” with l1-norm, which converts the inverse problem into a convex optimization problem. We seek accelerated sparse solution to nearfield multiple-input-multiple-output (MIMO) radar imaging problem For this purpose, we initially construct the problem as a convex optimization problem with sparsity (l1-norm and TV regularization) and solve it by using the augmented Lagrangian framework. The novelty of this study is to develop efficient sparsity-based reconstruction methods that exploit FMM formulation for matrix-vector multiplications involved, enabling significant reduction in computation time and memory requirement.

FORWARD PROBLEM

INVERSE PROBLEM

RECONSTRUCTION ALGORITHMS

C-SALSA-2

NUMERICAL RESULTS

CONCLUSION