Performance Analysis of Compressive-Sensing-Based Through-the-Wall Imaging with Effect of Unknown Parameters

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 and generate high-resolution images. Although current works apply CS directly to TWI, questions on the required number of measurements for a sparsity level, measurement strategy to subsample in frequency and space, or imaging performance in varying noise levels and limits on CS range resolution performance still needs to be answered. In addition current CS-based imaging methods are based on two basic assumptions; targets are point like and positioned at only discrete 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 extends the theory of CS-based radar imaging developed for subsurface imaging to TWI and outlines the performance of the proposed imaging for the above-mentioned questions using numerical simulations. The effect of unknown parameters on the imaging performance is analyzed, and it is observed that off-the-grid point targets and big modeling errors decreases the performance of CS imaging.