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Reconstruction of the complex refractive index in nonlinear phase contrast tomography. (English) Zbl 1329.92069

Summary: A new nonlinear method to reconstruct the complex refractive index distribution with in-line phase tomography measurements is presented. The inverse problem is regularized with the Tikhonov smoothing \(L_2\) norm of the index. The original nonlinear iterative approach is based on the Fréchet derivative of the intensity recorded at a single propagation distance and on a Simultaneous Algebraic Reconstruction technique. The reconstruction method requires no a priori knowledge about the materials. The algorithm is successfully applied to some simulated data with noise.

MSC:

92C55 Biomedical imaging and signal processing
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
65J22 Numerical solution to inverse problems in abstract spaces
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