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.

Artifact free signal denoising with wavelets

Abstract: Recent years have seen the development of signal denoising algorithms based on the wavelet transform. It has been shown that thresholding the wavelet coefficients of a noisy signal allows us to restore the smoothness of the original signal. However, wavelet denoising suffers a main drawback: around discontinuities the reconstructed signal is smoothed, exhibiting the pseudo-Gibbs phenomenon. We consider the problem of denoising piecewise smooth signals with sharp discontinuities. We propose to apply a traditional wavelet denoising method and to restore the denoised signal using a total variation minimization approach. This second step allows us to remove the Gibbs phenomena and therefore to restore sharp discontinuities, while the other structures are preserved. The main innovation of our algorithm is to constrain the total variation minimization by the knowledge of the remaining wavelet coefficients. In this way, we make sure that the restoration process does not deteriorate the information that has been considered as significant in the denoising step. With this approach we substantially improve the performance of classical wavelet denoising algorithms, both in terms of SNR and in terms of visual artifacts.

A note on multi-image denoising

Abstract: Taking photographs under low light conditions with a hand-held camera is problematic. A long exposure time can cause motion blur due to the camera shaking and a short exposure time gives a noisy image. We consider the new technical possibility offered by cameras that take image bursts. Each image of the burst is sharp but noisy. In this preliminary investigation, we explore a strategy to efficiently denoise multi-images or video. The proposed algorithm is a complex image processing chain involving accurate registration, video equalization, noise estimation and the use of state-of-the-art denoising methods. Yet, we show that this complex chain may become risk free thanks to a key feature: the noise model can be estimated accurately from the image burst. Preliminary tests will be presented. On the technical side, the method can already be used to estimate a non parametric camera noise model from any image burst.

Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy.

Abstract: The localization of surface second-harmonic generation (S-SHG) enhancements from granular gold structures that exhibit local plasmon resonance was investigated. A two-photon microscopy technique was used to perform high spatial resolution S-SHG imaging. The magnitude and the spatial density of S-SHG enhancement confined in submicroscopic regions are strongly dependent on the morphology of the gold's surface. Polarization measurements of local S-SHG responses reveal the local field anisotropy in enhancement regions and furthermore prove the incoherent and strongly depolarized nature of the emission, which is attributed to ultrafast fluctuations of the enhancement location in the focal volume.

Multiscale Image Blind Denoising

Abstract: Arguably several thousands papers are dedicated to image denoising. Most papers assume a fixed noise model, mainly white Gaussian or Poissonian. This assumption is only valid for raw images. Yet, in most images handled by the public and even by scientists, the noise model is imperfectly known or unknown. End users only dispose the result of a complex image processing chain effectuated by uncontrolled hardware and software (and sometimes by chemical means). For such images, recent progress in noise estimation permits to estimate from a single image a noise model, which is simultaneously signal and frequency dependent. We propose here a multiscale denoising algorithm adapted to this broad noise model. This leads to a blind denoising algorithm which we demonstrate on real JPEG images and on scans of old photographs for which the formation model is unknown. The consistency of this algorithm is also verified on simulated distorted images. This algorithm is finally compared with the unique state of the art previous blind denoising method.

A rigorous derivation of a free-boundary problem arising in superconductivity

Abstract: We study the Ginzburg–Landau energy of superconductors submitted to a possibly non-uniform magnetic field, in the limit of a large Ginzburg–Landau parameter κ . We prove that the induced magnetic fields associated to minimizers of the energy-functional converge as κ →+∞ to the solution of a free-boundary problem. This free-boundary problem has a nontrivial solution only when the applied magnetic field is of the order of the “first critical field”, i.e. of the order of log κ . In other cases, our results are contained in those we had previously obtained [15, 16, 14]. We also derive a convergence result for the density of vortices.