Multistatic MIMO Sparse Imaging Based on FFT and Low-Rank Matrix Recovery Techniques

Abstract

This article proposes a simple sparse imaging scheme using a linear sparse aperiodic array and a new fast Fourier transform matched filtering (FFTMF) algorithm for a THz multistatic multiple-input and multiple-output (MIMO) imaging system. The simple linear sparse aperiodic array and multipass interferometric synthetic aperture focusing technique are used to achieve fast sampling, low system cost, and high imaging performance. Unlike a traditional generalized synthetic aperture focusing technique (GSAFT) for multistatic MIMO imaging, which is time-consuming and exhibits increased reconstruction time with increased data volume, the proposed FFTMF image reconstruction algorithm is capable of providing comparable image quality but significantly reducing the reconstruction time. For example, we show that for an image of 300 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times320$ </tex-math></inline-formula> mm with a pixel size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.75\times0.83$ </tex-math></inline-formula> mm, the reconstruction time is reduced from about 1.50 min to 0.25 s in the 220-GHz five-pass synthetic imaging experiments. The proposed imaging algorithm uses internal zero padding, a multipass interferometric synthetic aperture focusing technique, and a wideband imaging technique to improve the imaging performance under a low-cost, sparse sampling scheme. It shows a strong antinoise ability and a high tolerance to target focusing distance. In addition, integrated with an algorithm of principal component pursuit by alternating directions method (PCPADM), sparse imaging is available to further save system cost and sampling data without a loss of image quality while the novel use of an error matrix provides an additional detection capability for imaging systems.