Reconstruction algorithm for high contrast velocity travel time tomography
We consider travel time tomography problems involving detection of high contrast, discrete high velocity lines. This results in a discrete nonlinear inverse problem, for which traditional least-squares reconstruction algorithms are not suitable, as they tend to result in oscillations in the estimated values of the ray-path matrix. We propose a new algorithm that provides a more stable reconstruction for high contrast velocity scenarios. Our approach is based on using multiple candidate discrete high velocity lines along with a probabilistic mixture model that captures the likelihood of each of the lines. We propose an iterative algorithm based on a graphical model that successively updates the length and probability of these line structures. Preliminary simulation results show that exact reconstruction can be achieved in cases when the ground-truth lines are a subset of candidate structures.