LANDWEBER–KACZMARZ METHOD FOR INVERSE PROBLEMS USING MULTIPLE REPEATED MEASUREMENTS

This paper addresses Landweber–Kaczmarz method for solving linear or nonlinear system of inverse problems utilizing a general convex penalty function. Presume that noisy data which contains a deterministic noise level is unknown, and we reconstruct the solutions by averaging measurements obtained through multiple repeated experiments. In order to control the iteration process, our focus is on a new termination rule that relies on a modified version of the discrepancy principle. Theoretically, convergence analysis is presented. The regularization property is established from a statistical perspective. For visualizing the performance of the proposed method, we subsequently apply it to parameter identification problems and photoacoustic/thermoacoustic tomography. Experimental results demonstrate that our method performs well.