3-D imaging for ground penetrating radar using compressive sensing with block-toeplitz structures

Compressive sensing (CS) techniques have shown promise for sparse imaging applications such as ground penetrating radar (GPR). However, CS involves the enumeration of a dictionary which implies huge storage requirements when the problem is large and multidimensional. This paper shows that the underlying propagation model can have invariance properties that simplify the dictionary. Specifically, translational invariance in the GPR case leads to a block-Toeplitz structure that can be exploited to reduce both the storage, by a factor of N in each block-Toeplitz dimension, and the computational complexity. Exploiting this reduction in storage for the 3-dimensional GPR imaging problem makes the CS solution feasible for underground object detection.