Phase Estimation for Differential Interference Contrast Microscopy

Lola Bautista 1, 2
1 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : In this dissertation we address the problem of estimating the phase from color images acquired with differential–interference–contrast (DIC) microscopy. This technique has been widely recognized for producing high contrast images at high lateral resolution. One of its disadvantages is that the observed images cannot be easily used for topographical and morphological interpretation, because the changes in phase of the light, produced by variations in the refractive index of the object, are hidden in the intensity image. We present an image formation model for polychromatic light, along with a detailed description of the point spread function (PSF). As for the phase recovery problem, we followed the inverse problem approach by means of minimizing a non-linear least–squares (LS)–like discrepancy term with an edge–preserving regularizing term, given by either the hypersurface (HS) potential or the total variation (TV) one. We investigate the analytical properties of the resulting objective non-convex functions, prove the existence of minimizers and propose a compact formulation of the gradient allowing fast computations. Then we use recent effective optimization tools able to obtain in both the smooth and the non-smooth cases accurate reconstructions with a reduced computational demand. We performed different numerical tests on synthetic realistic images and we compared the proposed methods with both the original conjugate gradient method proposed in the literature, exploiting a gradient–free linesearch for the computation of the steplength parameter, and other standard conjugate gradient approaches. The results we obtained in this approach show that the performances of the limited memory gradient method used for minimizing the LS+HS functional are much better than those of the CG approaches in terms of number of function/gradient evaluations and, therefore, computational time. Then we also consider another formulation of the phase retrieval problem by means of minimization with respect to a complex variable under constraint of modulus one. However, standard projected gradient descent algorithms appear to be inefficient and sensitive to initialization. We conclude by proposing in this case a reformulation by optimization on low-rank matrices.
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Lola Bautista. Phase Estimation for Differential Interference Contrast Microscopy. Signal and Image processing. Université Côte d’Azur, Inria, CNRS, I3S, France, 2017. English. ⟨tel-01576339v1⟩

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