Analysis of unknown velocity and target off the grid problems in compressive sensing based subsurface imaging

Sparsity of target space in subsurface imaging problem is used within the framework of the compressive sensing (CS) theory in recent publications to decrease the data acquisition load in practical systems. The developed CS based imaging methods are based on two important assumptions; namely, that the speed of propagation in the medium is known and that potential targets are point like targets positioned at discrete spatial points. However, in most subsurface imaging problems these assumptions are not always valid. The propagation velocity may only be known approximately, and targets will generally not fall on the grid exactly. In this work, the performance of the CS based subsurface imaging methods are analyzed for the above defined problems and possible solutions are discussed.