Sequential subspace optimization for nonlinear inverse problems

Abstract

Abstract In this work we discuss a method to adapt sequential subspace optimization (SESOP), which has so far been developed for linear inverse problems in Hilbert and Banach spaces, to the case of nonlinear inverse problems. We start by revising the technique for linear problems. In a next step, we introduce a method using multiple search directions that are especially designed to fit the nonlinearity of the forward operator. To this end, we iteratively project the initial value onto stripes whose width is determined by the search direction, the nonlinearity of the operator and the noise level. We additionally propose a fast algorithm that uses two search directions. Finally, we will show convergence and regularization properties for the presented method.