Publications de Julien René Fageot

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This paper studies the continuous-domain inverse problem of recovering Radon measures on the one-dimensional torus from low-frequency Fourier coefficients, where K (c) is the cutoff frequency. Our approach consists in minimizing the total-variation norm am ...

Assessing the individual risk of Major Adverse Cardiac Events (MACE) is of major importance as cardiovascular diseases remain the leading cause of death worldwide. Quantitative Myocardial Perfusion Imaging (MPI) parameters such as stress Myocardial Blood F ...

In contrast to their seemingly simple and shared structure of independence and stationarity, Levy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes. Inspired by the recent p ...

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

A convolution algebra is a topological vector space X that is closed under the convolution operation. It is said to be inverse-closed if each element of X whose spectrum is bounded away from zero has a convolution inverse that is also part of the algebra. ...

In this paper, we perform the joint study of scale -invariant operators and self -similar processes of complex order. More precisely, we introduce general families of scale -invariant complex -order fractional -derivation and integration operators by const ...

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions of the Fourier samples of the ground truth up to a maximum cutoff frequency ...

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape ...

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical ...

We study continuous-domain linear inverse problems with generalized total-variation (gTV) regularization, expressed in terms of a regularization operator L. It has recently been proved that such inverse problems have sparse spline solutions, with fewer jum ...

The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated in the literature, and their localization and detection properties are well ...

In this paper, we precisely quantify the wavelet compressibility of compound Poisson processes. To that end, we expand the given random process over the Haar wavelet basis and we analyse its asymptotic approximation properties. By only considering the nonz ...

Julien René Fageot

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On the uniqueness of solutions for the basis pursuit in the continuum

Comparing various AI approaches to traditional quantitative assessment of the myocardial perfusion in [82Rb] PET for MACE prediction

Entropic Compressibility of Levy Processes

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters

Complex-order scale-invariant operators and self-similar processes

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility

TV-based spline reconstruction with Fourier measurements: Uniqueness and convergence of grid-based methods

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

The n-term Approximation of Periodic Generalized Levy Processes

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Gaussian and sparse processes are limits of generalized Poisson processes

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Support and approximation properties of Hermite splines

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization

Angular Accuracy of Steerable Feature Detectors

The Wavelet Compressibility of Compound Poisson Processes