Two-stage through-the-wall radar image formation using compressive sensing

We introduce a robust image-formation approach for through-the-wall radar imaging (TWRI). The proposed approach consists of two stages involving compressive sensing (CS) followed by delay-and-sum (DS) beamforming. In the first stage, CS is used to reconstruct a complete set of measurements from a small subset collected with a reduced number of transceivers and frequencies. DS beamforming is then applied to form the image using the reconstructed measurements. To promote sparsity of the CS solution, an overcomplete Gabor dictionary is employed to sparsely represent the imaged scene. The new approach requires far fewer measurement samples than the conventional DS beamforming and CSbased TWRI methods to reconstruct a high-quality image of the scene. Experimental results based on simulated and real data demonstrate the effectiveness and robustness of the proposed two-stage image formation technique, especially when the measurement set is drastically reduced.