Publications by Julien René Pierre Fageot

Gaussian versus Sparse Stochastic Processes

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 ...

EPFL2017

On the Besov regularity of periodic Levy noises

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

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 ...

Academic Press Inc Elsevier Science2017

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

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

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 ...

2017

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Michaël Unser, Julien René Pierre Fageot, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

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 ...

2017

Hermite Snakes with Control of Tangents

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann

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. ...

IEEE2016

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

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

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 ...

IEEE2016

Compressibility of Symmetric-α-Stable Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

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 ...

IEEE2015

Wavelet Statistics of Sparse and Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

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 ...

Siam Publications2015

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

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 ...

IEEE2015

Statistical Optimality of Hermite Splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Harshit Gupta

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 ...

IEEE2015

Julien René Pierre Fageot

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Gaussian versus Sparse Stochastic Processes

On the Besov regularity of periodic Levy noises

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

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Hermite Snakes with Control of Tangents

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

Compressibility of Symmetric-α-Stable Processes

Wavelet Statistics of Sparse and Self-Similar Images

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

Statistical Optimality of Hermite Splines

Gaussian versus Sparse Stochastic Processes

On the Besov regularity of periodic Levy noises

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

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

Hermite Snakes with Control of Tangents

Compressibility of Symmetric-α-Stable Processes

Wavelet Statistics of Sparse and Self-Similar Images

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Statistical Optimality of Hermite Splines