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.

LTL with the Freeze Quantifier and Register Automata

Abstract: A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. To reason about data words, linear temporal logic is extended by the freeze quantifier, which stores the element at the current word position into a register, for equality comparisons deeper in the formula. By translations from the logic to alternating automata with registers and then to faulty counter automata whose counters may erroneously increase at any time, and from faulty and error-free counter automata to the logic, we obtain a complete complexity table for logical fragments defined by varying the set of temporal operators and the number of registers. In particular, the logic with future-time operators and 1 register is decidable but not primitive recursive over finite data words. Adding past-time operators or 1 more register, or switching to infinite data words, cause undecidability.

Secrets of image denoising cuisine

Abstract: Digital images are matrices of equally spaced pixels, each containing a photon count. This photon count is a stochastic process due to the quantum nature of light. It follows that all images are noisy. Ever since digital images have existed, numerical methods have been proposed to improve the signal-to-noise ratio. Such ‘denoising’ methods require a noise model and an image model. It is relatively easy to obtain a noise model. As will be explained in the present paper, it is even possible to estimate it from a single noisy image.

Texture classification using windowed Fourier filters

Abstract: We define a distance between textures for texture classification from texture features based on windowed Fourier filters. The definition of the distance relies on an interpretation of our texture attributes in terms of spectral density when the texture can be considered as a Gaussian random field. The distance between textures is then defined as a symmetrized Kullback distance which is a simple function of the attributes and does not require any normalization. An experimental analysis using Gabor filters, and in particular a comparison to quadratic distances, shows the efficiency and robustness of the method.

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Abstract: We consider the restoration of piecewise constant images where the number of the regions and their values are not fixed in advance, with a good difference of piecewise constant values between neighboring regions, from noisy data obtained at the output of a linear operator (e.g., a blurring kernel or a Radon transform). Thus we also address the generic problem of unsupervised segmentation in the context of linear inverse problems. The segmentation and the restoration tasks are solved jointly by minimizing an objective function (an energy) composed of a quadratic data-fidelity term and a nonsmooth nonconvex regularization term. The pertinence of such an energy is ensured by the analytical properties of its minimizers. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonsmooth nonconvex minimization. Indeed, the existing methods are unsatisfactory since they (implicitly or explicitly) involve a smooth approximation of the regularization term and often get stuck in shallow local minima. The goal of this paper is to design a method that efficiently handles the nonsmooth nonconvex minimization. More precisely, we propose a continuation method where one tracks the minimizers along a sequence of approximate nonsmooth energies $\{J_\eps\}$, the first of which being strictly convex and the last one the original energy to minimize. Knowing the importance of the nonsmoothness of the regularization term for the segmentation task, each $J_\eps$ is nonsmooth and is expressed as the sum of an $\ell_1$ regularization term and a smooth nonconvex function. Furthermore, the local minimization of each $J_{\eps}$ is reformulated as the minimization of a smooth function subject to a set of linear constraints. The latter problem is solved by the modified primal-dual interior point method, which guarantees the descent direction at each step. Experimental results are presented and show the effectiveness and the efficiency of the proposed method. Comparison with simulated annealing methods further shows the advantage of our method.

A mesoporous silica functionalized by a covalently bound calixarene-based fluoroionophore for selective optical sensing of mercury(II) in water

Abstract: With the aim of optical sensing of Hg2+ in water, a calixarene bearing two dansyl fluorophores was grafted on a large pore mesoporous silica material (SBA-15) via two long alkyl chains containing triethoxysilane groups. The characterization of the obtained material 2-SBA-15 shows that the organized structure is preserved after the post-grafting procedure. A detailed study of the complexing and fluorescence properties of 2-SBA-15 is reported. The functionalized material is able to reversibly detect Hg2+ with a response time of a few seconds and a detection limit of 3.3 × 10−7 mol L−1 in water. Furthermore, this system offers a high selectivity over several interfering cations (Na+, K+, Ca2+, Cu2+, Cd2+, Pb2+).