Abstract

We propose a nonlinear primal–dual algorithm for the retrieval of phase shift and absorption from a single x ray in-line phase contrast, or Fresnel diffraction, image. The algorithm permits us to regularize phase and absorption separately. We demonstrate that taking into account the nonlinearity in the reconstruction improves reconstruction compared with linear methods. We also demonstrate that choosing different regularizers for absorption and phase can improve the reconstructions. The use of the total variation and its generalization in a primal–dual approach allows us to exploit the sparsity of the investigated sample. On both simulated and real datasets, the proposed nonlinear primal–dual hybrid gradient (NL-PDHG) method yields reconstructions with considerably fewer artifacts and improved the normalized mean squared error compared with its linearized version.

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