Controlled wavelet domain sparsity for x-ray tomography

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http://hdl.handle.net/10138/237217

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Purisha , Z , Rimpeläinen , J , Bubba , T & Siltanen , S 2018 , ' Controlled wavelet domain sparsity for x-ray tomography ' , Measurement Science and Technology , vol. 29 , no. 1 , 014002 . https://doi.org/10.1088/1361-6501/aa9260

Title: Controlled wavelet domain sparsity for x-ray tomography
Author: Purisha, Zenith; Rimpeläinen, Juho; Bubba, Tatiana; Siltanen, Samuli
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018-01
Language: eng
Number of pages: 9
Belongs to series: Measurement Science and Technology
ISSN: 0957-0233
URI: http://hdl.handle.net/10138/237217
Abstract: Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This, in turn, can be achieved by variational regularization, where the penalty term is the sum of the absolute values of the wavelet coefficients. The primal-dual fixed point algorithm showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter mu > 0 is analogous to the notoriously difficult problem of picking the optimal regularization parameter in Tikhonov regularization. Here, a novel automatic method is introduced for choosing mu, based on a control algorithm driving the sparsity of the reconstruction to an a priori known ratio of nonzero versus zero wavelet coefficients in the unknown.
Subject: 111 Mathematics
sparsity
wavelet
regularization
control
limited data tomography
x-ray tomography
REGULARIZATION PARAMETER
IMAGE-RESTORATION
ALGORITHM
MINIMIZATION
CHOICE
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