On unifying randomized approaches in inverse problems

Major Activities

Randomized Inverse Problems

We have developed a unified framework under which we can study and understand randomized approaches to solving inverse and other optimization problems. We show that various randomized approaches to solving inverse problems can be viewed as special cases of this more general framework. In particular, we prove asymptotic and non-asymptotic convergence results for a broad class of randomizations using stochastic optimization theory.

Significant Results

We analyze numerically the advantages of sketching the forward map from the left compared to sketching from the right and compare results. For the Shaw problem (P.C. Hansen, Regularization tools version 4.0), we see that the randomized MAP (Wang, Bui-Thanh, Ghattas) and left sketching approaches perform well with few samples while right sketching performs poorly. We study this phenomenon from the viewpoint of regularization.