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

Inverse Analysis of Radiative Flux Maps for the Characterization of High Flux Sources

Sophia Haussener, Clemens Gregor Suter, Gaël Jean Clément Levêque

The reconstruction of the angular and spatial intensity distribution from radiative flux maps measured in high flux solar simulators or optical concentrators is an ill-posed inverse problem requiring special solution strategies. We aimed at providing a sol ...

2019

Stationary time-vertex signal processing

Nathanaël Perraudin, Andreas Loukas

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some known graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that g ...

2019

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Martin Vetterli, Thierry Blu, Hanjie Pan

It is a classic problem to estimate continuous-time sparse signals, like point sources in a direction-of-arrival problem, or pulses in a time-of-flight measurement. The earliest occurrence is the estimation of sinusoids in time series using Prony's method. ...

Institute of Electrical and Electronics Engineers2017

Smoothing technique for nonsmooth composite minimization with linear operator

Volkan Cevher, Van Quang Nguyen

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap technique. In addition t ...

2017

Gaussian versus Sparse Stochastic Processes

Julien René Pierre Fageot

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

Towards Stationary Time-Vertex Signal Processing

Pierre Vandergheynst, Nathanaël Perraudin, Andreas Loukas, Francesco Grassi

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods ...

Ieee2017

Fréchet means in Wasserstein space

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017

Towards stationary time-vertex signal processing

Pierre Vandergheynst, Nathanaël Perraudin, Andreas Loukas, Francesco Grassi

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods ...

2016

How does one compute the noise power to simulate real and complex GNSS signals?

Cyril Botteron, Jérôme Leclère

Simulation of GNSS signals is very important to test and validate algorithms. With some algorithms, such as acquisition or tracking, we do not need to simulate a realistic constellation with actual ranges, Doppler or navigation data. We can simply simulate ...

2016

Convolutional Neural Networks on Graphs and Stationarity

The Fourier spectrum is often not sufficient to discriminate complex signals because it does not take into account higher-order moments. Wide Sense Stationarity is for sure not sufficient to characterize the signal as it considers only moments of order 2. ...

2016

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

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Inverse Analysis of Radiative Flux Maps for the Characterization of High Flux Sources

Stationary time-vertex signal processing

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Smoothing technique for nonsmooth composite minimization with linear operator

Gaussian versus Sparse Stochastic Processes

Towards Stationary Time-Vertex Signal Processing

Fréchet means in Wasserstein space

Towards stationary time-vertex signal processing

How does one compute the noise power to simulate real and complex GNSS signals?

Convolutional Neural Networks on Graphs and Stationarity

How does one compute the noise power to simulate real and complex GNSS signals?

Towards Stationary Time-Vertex Signal Processing

Convolutional Neural Networks on Graphs and Stationarity

Inverse Analysis of Radiative Flux Maps for the Characterization of High Flux Sources

Smoothing technique for nonsmooth composite minimization with linear operator

Stationary time-vertex signal processing

Fréchet means in Wasserstein space

Gaussian versus Sparse Stochastic Processes

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Towards stationary time-vertex signal processing