The aim of this paper is to investigate an inverse problem recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such ill-posed and has important practical applications. For problem, we propose general regularization method based on the idea filter method. With suitable condition, prove that optimal under various choices pa...

In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on assumption that mapping satisfies Hölder stability estimate locally. We consider both noisy as well non-noisy data our analysis. Under a-priori choice stopping index data, we show iterates remain a cert...

Infinite two-player games constitute a powerful and flexible framework for the design and verification of reactive systems. It is well-known that, for example, the construction of a controller acting indefinitely within its environment can be reduced to the computation of a winning strategy in an infinite game (Pnueli and Rosner, 1989). For the class of regular games, Büchi and Landweber (1969)...

In infrared astronomy, an observed image from a chop and nod process can be considered as the result of passing the original image through a highpass filter. Here we propose a restoration algorithm which builds up a tight framelet system that has the highpass filter as one of the framelet filters. Our approach reduces the solution of restoration problem to that of recovering the missing coeffic...

In this work we present and analyze a Kaczmarz version of the iterative regularization scheme REGINN-Landweber for nonlinear ill-posed problems in Banach spaces [Jin, Inverse Problems 28(2012), 065002]. Kaczmarz methods are designed for problems which split into smaller subproblems which are then processed cyclically during each iteration step. Under standard assumptions on the Banach space and...