ABSORPTION AND PHASE RETRIEVAL WITH TIKHONOV AND JOINT SPARSITY REGULARIZATIONS

作者：Sixou Bruno^*; Davidoiu Valentina; Langer Max; Peyrin Francosie

来源：Inverse Problems and Imaging, 2013, 7(1): 267-282.

DOI：10.3934/ipi.2013.7.267

• Nonlinear inverse problems
• phase retrieval
• Tikhonov regularization
• joint sparsity
• Gauss-Newton mehtod
• biomedical imaging

The X-ray phase contrast imaging technique relies on the measurement of the Fresnel diffraction intensity patterns associated to a phase shift induced by the object. The simultaneous recovery of the phase and of the absorption is an ill-posed nonlinear inverse problem. In this work, we investigate the resolution of this problem with nonlinear Tikhonov regularization and with a joint sparsity constraint regularization. The regularization functionals are minimized with a Gauss-Newton method and with a fixed point iterative method based on a surrogate functional. The algorithms are evalutated using simulated noisy data. The joint sparsity regularization gives better reconstructions for high noise levels.

• 出版日期2013-2