Publications de Julien René Fageot

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We consider the reconstruction of multi-dimensional signals from noisy samples. The problem is formulated within the framework of the theory of continuous-domain sparse stochastic processes. In particular, we study the fractional Laplacian as the whitening ...

Context. Imaging in radio interferometry requires solving an ill-posed noisy inverse problem, for which the most adopted algorithm is the original CLEAN algorithm and its variants. Alternative explicit optimization methods have gained increasing attention, ...

In this paper, we study the Besov regularity of Levy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for gene ...

In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrab ...

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown positions and orientations that we aim at retrieving. W ...

Motivation: Rotated template matching is an efficient and versatile algorithm to analyze microscopy images, as it automates the detection of stereotypical structures, such as organelles that can appear at any orientation. Its performance however quickly de ...

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by con ...

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing r ...

We study continuous-domain linear inverse problems that involve a general data-fidelity term and a regularisation term. We consider a regularisation that is formed by the sparsity-promoting total-variation norm, pre-composed with a differential operator th ...

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

We define and investigate the Local Rotation Invariance (LRI) and Directional Sensitivity (DS) of radiomics features. Most of the classical features cannot combine the two properties, which are antagonist in simple designs. We propose texture operators bas ...

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

We consider the class of continuous-time autoregressive (CAR) processes driven by (possibly non-Gaussian) Lévy white noises. When the excitation is an impulsive noise, also known as compound Poisson noise, the associated CAR process is a random non-uniform ...

Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. Fi ...

We introduce a new model of parametric contours defined in a continuous fashion. Our curve model relies on Hermite spline interpolation and can easily generate curves with sharp discontinuities; it also grants direct access to the tangent at each location. ...

We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a different regularizati ...

Nous nous intéressons à la reconstruction parcimonieuse d’images à l’aide du problème d’optimisation régularisé LASSO. Dans de nombreuses applications pratiques, les grandes dimensions des objets à reconstruire limitent, voire empêchent, l’utilisation des ...

Julien René Fageot

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MAP Estimators for Self-Similar Sparse Stochastic Models

PolyCLEAN: Atomic optimization for super-resolution imaging and uncertainty estimation in radio interferometry

On the Besov regularity of periodic Levy noises

Multidimensional Lévy White Noise in Weighted Besov Spaces

Principled Design and Implementation of Steerable Detectors

Steer'n'Detect: fast 2D template detection with accurate orientation estimation

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Statistical Optimality of Hermite Splines

Convergence analysis of the discretization of continuous-domain inverse problems

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

Wavelet Statistics of Sparse and Self-Similar Images

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

Compressibility of Symmetric-α-Stable Processes

Hermite Snakes with Control of Tangents

A Decoupled Approach for Composite Sparse-plus-Smooth Penalized Optimization

Une version polyatomique de l'algorithme Frank-Wolfe pour résoudre le problème LASSO en grandes dimensions