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PhD



Image Restoration in the presence of Poisson-Gaussian noise [TEL]

The thesis deals with the restoration of images corrupted by blur and noise, with emphasis on confocal microscopy and macroscopy applications.

Due to low photon count and high detector noise, the Poisson-Gaussian model is well suited to this context. However, up to now it had not been widely utilized because of theoretical and practical difficulties. In view of this, we formulate the image restoration problem in the presence of Poisson-Gaussian noise in a variational framework, where we express and study the exact data fidelity term. The solution to the problem can also be interpreted as a Maximum A Posteriori (MAP) estimate. Using recent primal-dual convex optimization algorithms, we obtain results that outperform methods relying on a variety of approximations.

Turning our attention to the regularization term in the MAP framework, we study both discrete and continuous approximations of the $\ell_0$ pseudo-norm. This useful measure, well-known for promoting sparsity, is difficult to optimize due to its non-convexity and its non-smoothness. We propose an efficient graph-cut procedure for optimizing energies with truncated quadratic priors. Moreover, we develop a majorize-minimize memory gradient algorithm to optimize various smooth versions of the $\ell_2-\ell_0$ norm, with guaranteed convergence properties. In particular, good results are achieved on deconvolution problems.

One difficulty with variational formulations is the necessity to tune automatically the model hyperparameters. In this context, we propose to estimate the Poisson-Gaussian noise parameters based on two realistic scenarios: one from time series images, taking into account bleaching effects, and another from a single image. These estimations are grounded on the use of an Expectation-Maximization (EM) approach.

Overall, this thesis proposes and evaluates various methodologies for tackling difficult image noise and blur cases, which should be useful in various applicative contexts within and beyond microscopy.



Supervisors



Jury

Polish Academy of Sciences

Systems Research Institute
Department of Modelling and Optimization of Dynamical Systems
Newelska 6, 01-447 Warsaw, Poland
Anna.Jezierska@ibspan.waw.pl anna.jezierska@univ-paris-est.fr