Analysis of compressive sensing based through the wall imaging

Compressive sensing (CS) has been shown to be a useful tool for subsurface or through the wall imaging (TWI) using ground penetrating radar (GPR). It has been used to decrease both time/frequency or spatial measurements or to generate high resolution images. Although current works apply CS to TWI, they lack analysis for CS about the required number of measurements for sparsity levels, imaging performance in varying noise levels or performance of different measurement strategies. In addition proposed CS based imaging methods are based on two basic assumptions; targets are point like positioned at only discrete spatial or grid locations and wall thickness and its dielectric constant are perfectly known. However these assumptions are not usually valid in most TWI applications. This work details the theory for CS based TWI, analyzes the performance of the proposed imaging for the above mentioned cases. The effect of errors in unknown parameters on the imaging performance is analyzed and possible solutions are discussed.