A Universal Fast Back Projection Method for Nonuniform Sampling Based on Nonuniform FFT

Back projection (BP) is the basic method for most of radar imaging, such as synthetic aperture radar (SAR) imaging, through-the-wall imaging (TWI), ground penetrating radar (GPR) imaging, and etc. It also plays as an important role in the inverse scattering. For example, BP is an important iterative step in Born approximation based imaging and compressive-sensing-based imaging, and it is leading to a reasonable trial in nonlinear inverse scattering. The major problem of BP is that it is very time-consuming. However, when the imaging radar, i.e., the SIMO/MIMO radar, randomized sampling compressive sensing radar, has to take samples at uniform spatial points, the BP is seemed as the only choice. How to accelerate BP in the nonuniform sampling situation becomes a valuable problem. In this paper we propose a universal fast BP method for nonuniform sampling. The 'universal' means the proposed method is suitable for arbitrary displacement of the transmitters and the receivers, for arbitrary kind of T/R antennas, for far field and near field imaging, and for the freespace and multilayered environment. The method is based on the nonuniform FFT (NuFFT). It firstly transforms the nonuniform time-spatial samples to the uniform ω-k domain samples, secondly maps the uniform ω-k domain samples to the nonuniform spectrum domain samples, and finally transforms the nonuniform spectrum domain samples to the uniform sampled imaging. The NuFFT accelerates the process and reduces the complexity of BP from O(MN) to O(Mlog(MN)), where M and N is the samples and the unknowns, respectively. The experiment results shows the validity and the efficiency of the proposed method.