Total variation regularized velocity estimation to image subsurface reflectivity

We propose a modified frequency-wavenumber migration method to enhance subsurface imagery obtained by ground penetrating radar (GPR) array to localize buried landmines and other objects. The method aims to minimize the entropy of processed image by introducing different wave propagation velocity for each array element. The different wave propagation velocity is organized to form a velocity vector. On the other hand, by constraining the total variation of the velocity vector, the method satisfies physics requirement that the velocity shall not change abruptly. The optimization scheme is built in the framework of Tikhonov regularization by selecting proper regularization parameter. We use examples obtained from 2-D GPR images. The frequency-wavenumber method and its optimization can be generalized to 3-D in a straight-forward manner.