Multi-resolution parameter choice method for total variation regularized tomography

Niinimäki, Kati; Lassas, Matti; Hämäläinen, K.; Kallonen, Aki; Kolehmainen, Ville; Niemi, Esa; Siltanen, Samuli

doi:10.48550/arxiv.1407.2386

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“…Many approaches for the regularization parameter selection have been proposed. For a selection of methods designed for total variation (TV) regularization see the following studies: [5,6,7,8,9,10,11,12]. In this paper we introduce a novel automatic method for choosing µ based on a control algorithm driving the sparsity of the reconstruction to an a priori known ratio 0 ≤ C pr ≤ 1 of nonzero wavelet coefficients in f .…”

Section: Introductionmentioning

confidence: 99%

Controlled wavelet domain sparsity for x-ray tomography

Purisha

Rimpeläinen

Bubba

et al. 2017

Meas. Sci. Technol.

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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 (PDFP) algorithm introduced by Peijun Chen, Jianguo Huang, and Xiaoqun Zhang (Fixed Point Theory and Applications 2016) showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter µ > 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 µ, 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.

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