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Absorption and phase retrieval with Tikhonov and joint sparsity regularizations

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  • 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.
    Mathematics Subject Classification: Primary: 65J22, 65J20, 65K10; Secondary: 52A41.


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