
αℓ_1βℓ_2 sparsity regularization for nonlinear illposed problems
In this paper, we consider the α·_ℓ_1β·_ℓ_2 sparsity regularization wit...
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An ADMMNewtonCNN Numerical Approach to a TV Model for Identifying Discontinuous Diffusion Coefficients in Elliptic Equations: Convex Case with Gradient Observations
Identifying the discontinuous diffusion coefficient in an elliptic equat...
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A Regularization Operator for the Source Approximation of a Transport Equation
Source identification problems have multiple applications in engineering...
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Hessian SchattenNorm Regularization for Linear Inverse Problems
We introduce a novel family of invariant, convex, and nonquadratic func...
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On quasireversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates
We are interested in the classical illposed Cauchy problem for the Lapl...
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A variational nonlinear constrained model for the inversion of FDEM data
Reconstructing the structure of the soil using non invasive techniques i...
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Convergence analysis of a CrankNicolson Galerkin method for an inverse source problem for parabolic systems with boundary observations
This work is devoted to an inverse problem of identifying a source term ...
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Identifying source term in the subdiffusion equation with L^2TV regularization
In this paper, we consider the inverse source problem for the timefractional diffusion equation, which has been known to be an illposed problem. To deal with the illposedness of the problem, we propose to transform the problem into a regularized problem with L^2 and total variational (TV) regularization terms. Differing from the classical Tikhonov regularization with L^2 penalty terms, the TV regularization is beneficial for reconstructing discontinuous or piecewise constant solutions. The regularized problem is then approximated by a fully discrete scheme. Our theoretical results include: estimate of the error order between the discrete problem and the continuous direct problem; the convergence rate of the discrete regularized solution to the target source term; and the convergence of the regularized solution with respect to the noise level. Then we propose an accelerated primaldual iterative algorithm based on an equivalent saddlepoint reformulation of the discrete regularized model. Finally, a series of numerical tests are carried out to demonstrate the efficiency and accuracy of the algorithm.
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