We consider a general formulation of the problem signal reconstruction from incomplete priori information about it and measurements intensity its Fourier transform. Some special cases are studied when is even or odd part signal, as well real imaginary signal. Exact solutions in quadratures constructed. An algorithm for solving proposed only image intensities known.

We consider inverse problems in Hilbert spaces under correlated Gaussian noise, and use a Bayesian approach to find their regularized solution. focus on mildly ill-posed with fractional using novel wavelet-based vaguelette–vaguelette approach. It allows us apply sequence space methods without assuming that all operators are simultaneously diagonalizable. The results proved for more general base...

We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines regularizer consisting of penalty term that enforces regularity in the encoder domain, augmented by penalizes distance to signal manifold. present rigorous convergence analysis including stability estimates and rates. ...

This paper is focused on the optimization approach to solution of inverse problems. We introduce a stochastic dynamical system in which parameter-to-data map embedded, with goal employing techniques from nonlinear Kalman filtering estimate parameter given data. The extended filter (which we refer as ExKI context problems) can be effective for some problems approached this way, but impractical w...