Section: New Results

DIC (differential-interference-contrast) microscopy

Participants : Lola-Xiomara Bautista Rozo, Laure Blanc-Féraud.

This work is made in collaboration with Simone Rebegoldi, Marco Prato and Luca Zanni are in the Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Universita di Modena e Reggio Emilia, Modena, Italy.

he DIC (differential-interference-contrast) microscopy states the problem of image phase reconstruction which is ill-posed (under-determinated) and non-convex optimization problem. We have worked on the phase reconstruction from color images by optimization of a non linear least-squares-like discrepancy term regularized with a total variation functional. We have considered two different penalties, the first one being the total variation (TV) functional which is suitable for piecewise constant images, while the second is the hypersurface (HS) potential, which is a smooth generalization of the TV able to reconstruct both sharp and smooth variations of the unknown phase. Since the latter choice leads to the minimization of a smooth functional, we developed a limited memory gradient method, in which suitable adaptive steplength parameters are chosen to improve the convergence rate of the algorithm. As concerns the TV–based model, we addressed the minimization problem by means of a recently proposed linesearch–based forward–backward method able to handle the nonsmoothness of the TV functional. Numerical tests show that in the case of smooth TV minimization funcitonal, the performance of the limited memory gradient method is much better than those of the conjugate gradient approaches proposed in the literature, in terms of number of function/gradient evaluations and, therefore, computational time. In the case of TV functional, despite the difficulties due to the presence of a nondifferentiable term, also the linesearch–based forward–backward method proposed in this case is able to provide reconstructed images with a computational cost comparable to that of the gradient methods, thus leaving to a potential user freedom to choose the desired regularizer without losing in efficiency.

This work has been done during the PhD thesis of Lola Bautista defended in June 2017 [1]. It has been published in the journal Inverse Problems in 2017 [4].