Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Poisson noise reduction with non-local PCA

Abstract: Photon limitations arise in spectral imaging, nuclear medicine, astronomy and night vision. The Poisson distribution used to model this noise has variance equal to its mean so blind application of standard noise removals methods yields significant artifacts. Recently, overcomplete dictionaries combined with sparse learning techniques have become extremely popular in image reconstruction. The aim of the present work is to demonstrate that for the task of image denoising, nearly state-of-the-art results can be achieved using small dictionaries only, provided that they are learned directly from the noisy image. To this end, we introduce patch-based denoising algorithms which perform an adaptation of PCA (Principal Component Analysis) for Poisson noise. We carry out a comprehensive empirical evaluation of the performance of our algorithms in terms of accuracy when the photon count is really low. The results reveal that, despite its simplicity, PCA-flavored denoising appears to be competitive with other state-of-the-art denoising algorithms.

Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations

Abstract: The author investigates the value function of Mayer's problem arising in optimal control, and provides three equivalent definitions of lower semicontinuous solutions of the associated Hamilton-Jacobi-Bellman equation. Under quite weak assumptions about the control system, the value function is the unique solution. It coincides with the viscosity solution whenever it is continuous. >

Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation

Abstract: We consider here the value function corresponding to the optimal control of Zakai's equation and we study various regularity properties of this value function in the context of L2 distributions. In particular, we show that it is the unique viscosity solution of the corresponding infinite dimensionnal Hamilton-Jacobi-Bellman equation.