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1
Content available remote An Efficient Interpolation Approach for Exploring the Parameter Space of Regularized Tomography Algorithms
Lagerwerf Marinus J., Palenstijn Willem Jan, Bleichrodt Folkert, Batenburg K. Joost
Fundamenta Informaticae
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2020
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Vol. 172, nr 2
143--167
EN
Choosing a regularization parameter for tomographic reconstruction algorithms is often a cumbersome task of trial-and-error. Although several automatic and objective criteria have been proposed, each of them yields a different “optimal” value, which may or may not correspond to the actual implicit image quality metrics one would like to optimize for. Exploration of the space of regularization parameters is computationally expensive, as it requires many reconstructions to be computed. In this paper we propose an algorithmic approach for computationally efficient exploration of the regularization parameter space, based on a pixel-wise interpolation scheme. Once a relatively small number of reconstructions have been computed for a sparse sampling of the parameters, an approximation of the reconstructed image for other parameter values can be computed instantly, thereby allowing both manual and automated selection of the most preferable parameters based on a variety of image quality metrics. We demonstrate that for three common variational reconstruction methods, our approach results in accurate approximations of the reconstructed image and that it can be used in combination with existing approaches for choosing optimal regularization parameters.
2
Content available Restoration image degraded by a blurred variable in the field
Bentahar Y., Afifi M., Dalimi H., Amar S.
Optica Applicata
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2018
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Vol. 48, nr 1
5--14
EN
Various methods of deconvolution have been developed for several decades, notably in astronomy and microscopy. The extension of these techniques to the case of a spatially varied blur is currently an open problem. In this work, we consider a zone-invariant point spread function model to take into account blur variation in the image. Thus an algorithm has been used where the minimization of the criterion is performed in parallel on different areas of the image, while taking into account the estimates in the neighboring areas of the sub-images under consideration, so that the final solution is the minimum of the criterion where the blur is spatially varied.
3
Content available remote Phase Transitions and Cosparse Tomographic Recovery of Compound Solid Bodies from Few Projections
Denitiu A., Petra S., Schnörr C., Schnörr Ch.
Fundamenta Informaticae
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2014
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Vol. 135, nr 1/2
73--102
EN
We study unique recovery of cosparse signals from limited-view tomographic measurements of two- and three-dimensional domains. Admissible signals belong to the union of subspaces defined by all cosupports of maximal cardinality l with respect to the discrete gradient operator. We relate l both to the number of measurements and to a nullspace condition with respect to the measurement matrix, so as to achieve unique recovery by linear programming. These results are supported by comprehensive numerical experiments that show a high correlation of performance in practice and theoretical predictions. Despite poor properties of the measurement matrix from the viewpoint of compressed sensing, the class of uniquely recoverable signals basically seems large enough to cover practical applications, like contactless quality inspection of compound solid bodies composed of few materials.
4
Content available remote FPGA Embedded Implementation for Neutron Radiography Images Restoration Based on Tikhonov and TV Algorithms
Saadi S., Guessoum M., Bettayeb M.
Przegląd Elektrotechniczny
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2012
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R. 88, nr 11a
322-326
EN
In this paper, we present a mixed software/hardware Implementation for image restoration using Tikhonov and Total Variations (TV) approaches. The proposed work is implemented and compiled on the embedded development kit EDK6.3i and the synthesis software ISE6.3i available with Xilinx Virtex-II FPGA using C language. The proposed implementation is designed to be integrated in the whole imaging system and image enhancement results have been appreciated by neutron radiography final users. The design can significantly accelerate the two Algorithms.
PL
W artykule przedstawiono zastosowanie metod Tikhonova oraz Odchylenia Całkowitego w algorytmie odtwarzania obrazu. Do implementacji w języku C, wykorzystano płytę rozwojową EDK 6.3i z układem FPGA Virtex II Pro firmy Xilinx wraz z oprogramowaniem ISE 6.3i.
5
Content available remote The range of non-atomic measures on effect algebras
Khare M., Singh A. K.
Demonstratio Mathematica
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2010
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Vol. 43, nr 3
497-510
EN
The present paper deals with the study of superior variation m+, inferior variation m¯ and total variation |m| of an extended real-valued function m defined on an effect algebra L; having obtained a Jordan type decomposition theorem for a locally bounded real-valued measure m defined on L, we have observed that the range of a non-atomic function m defined on a D-lattice L is an interval (—m¯ (1), m+(1)). Finally, after introducing the notion of a relatively non-atomic measure on an effect algebra L, we have proved an analogue of Lyapunov convexity theorem for this measure.
6
Content available remote On the Kantorovich variant of generalized Bernstein type rational functions
Gupta V., Ispir N.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
117-130
EN
In the present paper we define Kantorovich variant of generalized Bernstein type rational functions. We establish the order of approximation for continuous functions in different normed spaces and also estimate the rate of convergence for functions of bounded variation.
7
Content available remote The rate of convergence by a new type of Meyer-König and Zeller operators
Gupta V., Abel U.
Fasciculi Mathematici
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2004
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Nr 34
15-23
EN
In the present paper we introduce a simple integral modification of Meyer-Konig and Zeller operators and study their rate of convergence, for functions of bounded variation.
8
Content available remote An estimate of the rate of convergence of a Bézier variant of the Baskakov-Kantorovich operators for bounded variation functions
Abel U., Gupta V.
Demonstratio Mathematica
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2003
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Vol. 36, nr 1
123--136
EN
In the present paper we introduce a Bézier variant of the Baskakov-Kantorovich operators and study the rate of convergence for functions of bounded variation. Furthermore, we present the complete asymptotic expansion for the Baskakov-Kantorovich operators.
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