Noise reduction by using interferometric measurements

The interferometric formulation of linear wave-based inversion problem was proposed by Demanet and Jugnon recently. Instead of directly fitting the data, they proposed to fit a subset of the data's cross-correlation. It can be verified that if the full cross-correlation is used, then the problem is equivalent to the usual least square problem. The subsampling, which is usually considered to cause instability to the solution, is surprisingly useful in this setting. Numerical experiments for the inverse source problem and the inverse scatting problem have both suggested that a 'good' sampling strategy can actually increase the stability under modeling error caused by the uncertainty of a kinetic nature. We will study the mathematical mechanism behind this phenomenon, and try to see whether or not there exists a universally 'good' sampling strategy independent of the types of forward operators we use.