S. Kindermann - Academia.edu (original) (raw)

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Abdul Wahab

Quaid-i-Azam University, Islamabad, Pakistan

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Papers by S. Kindermann

We consider the reconstruction of complex obstacles from few farfleld acoustic measure- ments. Th... more We consider the reconstruction of complex obstacles from few farfleld acoustic measure- ments. The complex obstacle is characterized by its shape and an impedance function dis- tributed along its boundary through Robin type boundary conditions. This is done by min- imizing an objective functional, which is the L2 distance between the given far fleld infor- mation g1 and the far

Numerical Functional Analysis and Optimization, 2006

In this paper, we consider new regularization methods for linear inverse problems of dynamic type... more In this paper, we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are followed: a continuous and a discrete one. We prove regularization properties and also obtain rates of convergence for the methods derived from both approaches. A numerical example concerning the dynamic EIT problem is used to illustrate the theoretical results.

Journal of Scientific Computing, 2006

In this paper we apply Y. Meyer's G-norm for image processing problems. We use a definition of th... more In this paper we apply Y. Meyer's G-norm for image processing problems. We use a definition of the G-norm as norm of linear functionals on BV , which seems to be more feasible for numerical computation. We establish the equivalence between Meyer's original definition and ours and show that computing the norm can be expressed as an interface problem. This allows us to define an algorithm based on the level set method for its solution. Alternatively we propose a fixed point method based on mean curvature type equations. A computation of the G-norm according to our definition additionally gives functions which can be used for denoising of simple structures in images under a high level of noise. We present some numerical computations of this denoising method which support this claim.

Journal of Inverse and Ill-posed Problems, 2007

We investigate continuous regularization methods for linear inverse problems of static and dynami... more We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization properties and also obtain rates of convergence for our methods. A numerical example concerning a dynamical electrical impedance tomography (EIT) problem is used to illustrate the theoretical results.

Applicable Analysis, 2007

Inverse Problems and Imaging, 2014

This article is devoted to the convergence analysis of a special family of iterative regularizati... more This article is devoted to the convergence analysis of a special family of iterative regularization methods for solving systems of ill-posed operator equations in Hilbert spaces, namely Kaczmarz-type methods. The analysis is focused on the Landweber-Kaczmarz (LK) explicit iteration and the iterated Tikhonov-Kaczmarz (iTK) implicit iteration. The corresponding symmetric versions of these iterative methods are also investigated (sLK and siTK). We prove convergence rates for the four methods above, extending and complementing the convergence analysis established originally in . 1 2 2 δ 2 .

We consider the reconstruction of complex obstacles from few farfleld acoustic measure- ments. Th... more We consider the reconstruction of complex obstacles from few farfleld acoustic measure- ments. The complex obstacle is characterized by its shape and an impedance function dis- tributed along its boundary through Robin type boundary conditions. This is done by min- imizing an objective functional, which is the L2 distance between the given far fleld infor- mation g1 and the far

Numerical Functional Analysis and Optimization, 2006

In this paper, we consider new regularization methods for linear inverse problems of dynamic type... more In this paper, we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are followed: a continuous and a discrete one. We prove regularization properties and also obtain rates of convergence for the methods derived from both approaches. A numerical example concerning the dynamic EIT problem is used to illustrate the theoretical results.

Journal of Scientific Computing, 2006

In this paper we apply Y. Meyer's G-norm for image processing problems. We use a definition of th... more In this paper we apply Y. Meyer's G-norm for image processing problems. We use a definition of the G-norm as norm of linear functionals on BV , which seems to be more feasible for numerical computation. We establish the equivalence between Meyer's original definition and ours and show that computing the norm can be expressed as an interface problem. This allows us to define an algorithm based on the level set method for its solution. Alternatively we propose a fixed point method based on mean curvature type equations. A computation of the G-norm according to our definition additionally gives functions which can be used for denoising of simple structures in images under a high level of noise. We present some numerical computations of this denoising method which support this claim.

Journal of Inverse and Ill-posed Problems, 2007

We investigate continuous regularization methods for linear inverse problems of static and dynami... more We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization properties and also obtain rates of convergence for our methods. A numerical example concerning a dynamical electrical impedance tomography (EIT) problem is used to illustrate the theoretical results.

Applicable Analysis, 2007

Inverse Problems and Imaging, 2014

This article is devoted to the convergence analysis of a special family of iterative regularizati... more This article is devoted to the convergence analysis of a special family of iterative regularization methods for solving systems of ill-posed operator equations in Hilbert spaces, namely Kaczmarz-type methods. The analysis is focused on the Landweber-Kaczmarz (LK) explicit iteration and the iterated Tikhonov-Kaczmarz (iTK) implicit iteration. The corresponding symmetric versions of these iterative methods are also investigated (sLK and siTK). We prove convergence rates for the four methods above, extending and complementing the convergence analysis established originally in . 1 2 2 δ 2 .

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