In this paper, we consider a generalized inexact Newton-Landweber iteration to solve nonlinear ill-posed inverse problems in Banach spaces, where the forward operator might not be Gâteaux differentiable. The method is designed with non-smooth convex penalty terms, including L1-like and total variation-like functionals, capture special features of solutions such as sparsity piecewise constancy. ...

An efficient nonlinear contrast source inversion scheme for electromagnetic imaging of sparse two-dimensional investigation domains is proposed. To avoid generating a sequence linear optimization problems, the non-linearity directly tackled using Landweber (NLW) iterations. A self-adaptive projected accelerated steepest descent (A-PASD) algorithm incorporated to enhance efficiency NLW The enfor...

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only finite-dimensional approximation of the measurements is available. For large class satisfying Lipschitz we show that same estimate holds even with finite number measurements. also derive globally convergent algorithm based on Landweber iteration. This theory appli...

Let C and Q be nonempty closed convex sets in RN and RM , respectively, and A an M by N real matrix. The split feasibility problem (SFP) is to find x ∈ C with Ax ∈ Q, if such x exist. An iterative method for solving the SFP, called the CQ algorithm, has the following iterative step: x = PC(x + γ A (PQ − I )Ax), where γ ∈ (0, 2/L) with L the largest eigenvalue of the matrix AT A and PC and PQ de...

In this paper, the inverse problems for boundary value and initial in a heat equation are posed solved. It is well known that those ill posed. The reformulated as integral equations of first kind by using separation-of-variables method. discretization allowed us to reduce system linear algebraic or operator on Hilbert spaces. Landweber-type iterative method was used order find an approximation ...

Compared with electrical resistance tomography, capacitively coupled tomography (CCERT) is preferred since it avoids problems of electrode corrosion and polarization. However, reconstruction conductivity distribution still a great challenge for CCERT. To improve quality, this work proposes novel image method based on total fractional-order variation regularization. Simulation conducted several ...

In this paper, we are interested in the problem of determining source function for Sobolev equation with fractional Laplacian. This is ill-posed sense Hadamard. order to edit instability solution, applied Landweber method. theoretical analysis results, show error estimate between exact solution and regularized by using an a priori regularization parameter choice rule posteriori rule. Finally, i...