A primal dual method for inverse problems in MRI with non-linear forward operators

Duration: 29 mins 32 secs

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Description:	Valkonen, T (University of Cambridge) Friday 07 February 2014, 14:30-15:00


Created:	2014-02-14 14:21
Collection:	Inference for Change-Point and Related Processes
Publisher:	Isaac Newton Institute
Copyright:	Valkonen, T
Language:	eng (English)


Abstract:	Co-authors: Martin Benning (University of Cambridge), Dan Holland (University of Cambridge), Lyn Gladden (University of Cambridge), Carola-Bibiane Schönlieb (University of Cambridge), Florian Knoll (New York University), Kristian Bredies (University of Graz) Many inverse problems inherently involve non-linear forward operators. In this talk, I concentrate on two examples from magnetic resonance imaging (MRI). One is modelling the Stejskal-Tanner equation in diffusion tensor imaging (DTI), and the other is decomposing a complex image into its phase and amplitude components for MR velocity imaging, in order to regularise them independently. The primal-dual method of Chambolle and Pock being advantageous for convex problems where sparsity in the image domain is modelled by total variation type functionals, I recently extended it to non-linear operators. Besides motivating the algorithm by the above applications, through earlier collaborative efforts using alternative convex models, I will sketch the main ingredients for proving local convergence of the method. Then I will demonstrate very promising numerical performance.

Abstract:

Co-authors: Martin Benning (University of Cambridge), Dan Holland (University of Cambridge), Lyn Gladden (University of Cambridge), Carola-Bibiane Schönlieb (University of Cambridge), Florian Knoll (New York University), Kristian Bredies (University of Graz)
Many inverse problems inherently involve non-linear forward operators. In this talk, I concentrate on two examples from magnetic resonance imaging (MRI). One is modelling the Stejskal-Tanner equation in diffusion tensor imaging (DTI), and the other is decomposing a complex image into its phase and amplitude components for MR velocity imaging, in order to regularise them independently. The primal-dual method of Chambolle and Pock being advantageous for convex problems where sparsity in the image domain is modelled by total variation type functionals, I recently extended it to non-linear operators. Besides motivating the algorithm by the above applications, through earlier collaborative efforts using alternative convex models, I will sketch the main ingredients for proving local convergence of the method. Then I will demonstrate very promising numerical performance.

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