École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients

Abstract: We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the multiplicative noise into additive noise (using a logarithmic function), apply a variational method on the log data or shrink their coefficients in a frame (e.g. a wavelet basis), and transform back the result using an exponential function. We propose a method composed of several stages: we use the log-image data and apply a reasonable under-optimal hard-thresholding on its curvelet transform; then we apply a variational method where we minimize a specialized hybrid criterion composed of an ? 1 data-fidelity to the thresholded coefficients and a Total Variation regularization (TV) term in the log-image domain; the restored image is an exponential of the obtained minimizer, weighted in a such way that the mean of the original image is preserved. Our restored images combine the advantages of shrinkage and variational methods and avoid their main drawbacks. Theoretical results on our hybrid criterion are presented. For the minimization stage, we propose a properly adapted fast scheme based on Douglas-Rachford splitting. The existence of a minimizer of our specialized criterion being proven, we demonstrate the convergence of the minimization scheme. The obtained numerical results clearly outperform the main alternative methods especially for images containing tricky geometrical structures.

Full counting statistics and phase diagram of a dissipative Rydberg gas.

Abstract: Ultracold gases excited to strongly interacting Rydberg states are a promising system for quantum simulations of many-body systems. For off-resonant excitation of such systems in the dissipative regime, highly correlated many-body states exhibiting, among other characteristics, intermittency and multimodal counting distributions are expected to be created. Here we report on the realization of a dissipative gas of rubidium Rydberg atoms and on the measurement of its full counting statistics and phase diagram for both resonant and off-resonant excitation. We find strongly bimodal counting distributions in the off-resonant regime that are compatible with intermittency due to the coexistence of dynamical phases. Our results pave the way towards detailed studies of many-body effects in Rydberg gases.