An Algorithm for the Proximity Operator in Hybrid TV-Wavelet Regularization, with Application to MR Image Reconstruction
Year: 2014
East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 1 : pp. 21–34
Abstract
Total variation (TV) and wavelet $L_1$ norms have often been used as regularization terms in image restoration and reconstruction problems. However, TV regularization can introduce staircase effects and wavelet regularization some ringing artifacts, but hybrid TV and wavelet regularization can reduce or remove these drawbacks in the reconstructed images. We need to compute the proximal operator of hybrid regularizations, which is generally a sub-problem in the optimization procedure. Both TV and wavelet $L_1$ regularisers are nonlinear and non-smooth, causing numerical difficulty. We propose a dual iterative approach to solve the minimization problem for hybrid regularizations and also prove the convergence of our proposed method, which we then apply to the problem of MR image reconstruction from highly random under-sampled k-space data. Numerical results show the efficiency and effectiveness of this proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.150413.260913a
East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 1 : pp. 21–34
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Total Variation (TV) wavelet regularization MR image.