A Bayesian fusion model for space-time reconstruction of finely resolved velocities in turbulent flows from low resolution measurements

The study of turbulent flows calls for measurements with high resolution both in space and in time. We propose a new approach to reconstruct High-Temporal-High-Spatial resolution velocity fields by combining two sources of information that are well-resolved either in space or in time, the Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS) resolution measurements. In the framework of co-conception between sensing and data post-processing, this work extensively investigates a Bayesian reconstruction approach using a simulated database. A Bayesian fusion model is developed to solve the inverse problem of data reconstruction. The model uses a Maximum A Posteriori estimate, which yields the most probable field knowing the measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds number is used to validate and assess the performances of the present approach. Low resolution measurements are subsampled in time and space from the fully resolved data. Reconstructed velocities are compared to the reference DNS to estimate the reconstruction errors. The model is compared to other conventional methods such as Linear Stochastic Estimation and cubic spline interpolation. Results show the superior accuracy of the proposed method in all configurations. Further investigations of model performances on various range of scales demonstrate its robustness. Numerical experiments also permit to estimate the expected maximum information level corresponding to limitations of experimental instruments.Comment: 15 pages, 6 figure

Spatio-angular Minimum-variance Tomographic Controller for Multi-Object Adaptive Optics systems

Multi-object astronomical adaptive-optics (MOAO) is now a mature wide-field observation mode to enlarge the adaptive-optics-corrected field in a few specific locations over tens of arc-minutes. The work-scope provided by open-loop tomography and pupil conjugation is amenable to a spatio-angular Linear-Quadratic Gaussian (SA-LQG) formulation aiming to provide enhanced correction across the field with improved performance over static reconstruction methods and less stringent computational complexity scaling laws. Starting from our previous work [1], we use stochastic time-progression models coupled to approximate sparse measurement operators to outline a suitable SA-LQG formulation capable of delivering near optimal correction. Under the spatio-angular framework the wave-fronts are never explicitly estimated in the volume,providing considerable computational savings on 10m-class telescopes and beyond. We find that for Raven, a 10m-class MOAO system with two science channels, the SA-LQG improves the limiting magnitude by two stellar magnitudes when both Strehl-ratio and Ensquared-energy are used as figures of merit. The sky-coverage is therefore improved by a factor of 5.Comment: 30 pages, 7 figures, submitted to Applied Optic

Three dimensional transparent structure segmentation and multiple 3D motion estimation from monocular perspective image sequences

A three dimensional scene can be segmented using different cues, such as boundaries, texture, motion, discontinuities of the optical flow, stereo, models for structure, etc. We investigate segmentation based upon one of these cues, namely three dimensional motion. If the scene contain transparent objects, the two dimensional (local) cues are inconsistent, since neighboring points with similar optical flow can correspond to different objects. We present a method for performing three dimensional motion-based segmentation of (possibly) transparent scenes together with recursive estimation of the motion of each independent rigid object from monocular perspective images. Our algorithm is based on a recently proposed method for rigid motion reconstruction and a validation test which allows us to initialize the scheme and detect outliers during the motion estimation procedure. The scheme is tested on challenging real and synthetic image sequences. Segmentation is performed for the Ullmann's experiment of two transparent cylinders rotating about the same axis in opposite directions