5,048 research outputs found
Kosiorek, Thomas M. interview
No full textOral History interview of Thomas M. Kosiorek. Interview conducted by Gabrielle Hanke and Roy McKinney
On the condition number of the antireflective transform
No full textDeconvolution problems with a finite observation window require appropriate models of the unknown signal in order to guarantee uniqueness of the solution. For this purpose it has recently been suggested to impose some kind of antireflectivity of the signal. With this constraint, the deconvolution problem can be solved with an appropriate modification of the fast sine transform, provided that the convolution kernel is symmetric. The corresponding transformation is called the antireflective transform. In this work we determine the condition number of the antireflective transform to first order, and use this to show that the so-called reblurring variant of Tikhonov regularization for deconvolution problems is a regularization method. Moreover, we establish upper bounds for the regularization error of the reblurring strategy that hold uniformly with respect to the size n of the algebraic system, even though the condition number of the antireflective transform grows with n. We briefly sketch how our results extend to higher space dimensions
Limmatathen im Aufbruch – Zürich und seine kulturelle Topografie im Zeitalter des Liberalismus
No full text
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring
No full textWe introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state of the art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional preconditioning
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