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- Christian Clason, Bangti Jin, Karl Kunisch
- SIAM J. Scientific Computing
- 2010

A novel splitting method is presented for the `1-TV restoration of degraded images subject to impulsive noise. The functional is split into an `2-TV denoising and an `1-`2 deblurring part. The dual problem of the relaxed functional is smooth with convex constraints, and can be solved efficiently by applying an Arrow-Hurwicz type algorithm to the augmented… (More)

- Bangti Jin, Raytcho D. Lazarov, Zhi Zhou
- SIAM J. Numerical Analysis
- 2013

We consider the initial boundary value problem for the homogeneous time-fractional diffusion equation ∂ t u − ∆u = 0 (0 < α < 1) with initial condition u(x, 0) = v(x) and a homogeneous Dirichlet boundary condition in a bounded polygonal domain Ω. We shall study two semidiscrete approximation schemes, i.e., Galerkin FEM and lumped mass Galerkin FEM, by using… (More)

- Kazufumi Ito, Bangti Jin, Tomoya Takeuchi
- SIAM J. Scientific Computing
- 2011

In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient… (More)

- Kazufumi Ito, Bangti Jin, Jun Zou
- 2013

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few… (More)

- Bangti Jin, Raytcho D. Lazarov, Zhi Zhou
- SIAM J. Numerical Analysis
- 2016

In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order α ∈ (3/2, 2) in the leading term and both convection and potential terms. They arise in the mathematical modeling of asymmetric super-diffusion processes in… (More)

We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced… (More)

- Matthias Gehre, Tobias Kluth, +4 authors Peter Maass
- J. Computational Applied Mathematics
- 2012

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l 1 and l regularization. The stability of the minimizer and its consistency are studied, and convergence rates for both a priori and a posteriori parameter choice rules are… (More)

- Kazufumi Ito, Bangti Jin, Tomoya Takeuchi
- ArXiv
- 2011

We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical… (More)

- Christian Clason, Bangti Jin, Karl Kunisch
- SIAM J. Imaging Sciences
- 2010

This paper considers the numerical solution of inverse problems with a L1 data fitting term, which is challenging due to the lack of differentiability of the objective functional. Utilizing convex duality, the problem is reformulated as minimizing a smooth functional with pointwise constraints, which can be efficiently solved using a semismooth Newton… (More)