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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are(More)
Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually incompatible with the physics of acquisition. To reflect the physical constraints of the imaging device, we introduce the(More)
Originating in Grenander's pattern theory, the problem of defining appropriate distances between shapes or images and the use of transformation groups to model the variability of natural images is now an active field of research. However, most of the existing results are stated in a deterministic setting while results in a random framework that are(More)
We define a notion of barycenter for random probability measures in the Wasserstein space. We study the population barycenter in terms of existence and uniqueness. Using a duality argument, we give a precise characterization of the population barycenter for compactly supported measures, and we make a connection between averaging in the Wasserstein space and(More)
In this paper we focus on extended Euclidean registration of a set of noisy images. We provide an appropriate statistical model for this kind of registration problems, and a new criterion based on Fourier-type transforms is proposed to estimate the translation, rotation and scaling parameters to align a set of images. This criterion is a two step procedure(More)
The goal of this paper is to review existing methods for protein mass spectrometry data analysis, and to present a new methodology for automatic extraction of significant peaks (biomarkers). For the pre-processing step required for data from MALDI-TOF or SELDI-TOF spectra, we use a purely nonparametric approach that combines stationary invariant wavelet(More)
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the process has a sparse representation in a large dictionary of basis functions. Using a matrix regression model, we(More)
The study of the correlations that may exist between neurophysiological signals is at the heart of modern techniques for data analysis in neuroscience. Wavelet coherence is a popular method to construct a time-frequency map that can be used to analyze the time-frequency correlations between two time series. Coherence is a normalized measure of dependence,(More)