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Learned Compressive Representations for Single-Photon 3D Imaging

Edoardo Charbon, Claudio Bruschini, Andrei Ardelean, Mohit Gupta

Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that ...

Ieee Computer Soc2023

The inductive bias of deep learning: Connecting weights and functions

Guillermo Ortiz Jimenez

Years of a fierce competition have naturally selected the fittest deep learning algorithms. Yet, although these models work well in practice, we still lack a proper characterization of why they do so. This poses serious questions about the robustness, trus ...

EPFL2023

A Structured Dictionary Perspective on Implicit Neural Representations

Pascal Frossard, Guillermo Ortiz Jimenez, Beril Besbinar, Gizem Yüce

Implicit neural representations (INRs) have recently emerged as a promising alternative to classical discretized representations of signals. Nevertheless, despite their practical success, we still do not understand how INRs represent signals. We propose a ...

IEEE COMPUTER SOC2022

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Thomas Jean Debarre

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

EPFL2022

Sparsest piecewise-linear regression of one-dimensional data

Michaël Unser, Julien René Pierre Fageot, Thomas Jean Debarre, Quentin Alain Denoyelle

We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there are efficient a ...

Elsevier2021

Multiple Line Outage Detection in Power Systems by Sparse Recovery Using Transient Data

Ping Hu, Feng Liu, Li Ding

Fast and accurate transmission line outage detection can help the central control unit to respond rapidly to better maintain the security and reliability of power systems. It is especially critical in the situation of multiple line outages which is more li ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Weak-lensing mass reconstruction using sparsity and a Gaussian random field

Austin Chandler Peel

Aims. We introduce a novel approach to reconstructing dark matter mass maps from weak gravitational lensing measurements. The cornerstone of the proposed method lies in a new modelling of the matter density field in the Universe as a mixture of two compone ...

2021

Multikernel Regression with Sparsity Constraint

Michaël Unser, Shayan Aziznejad

In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...

2021

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

SIAM PUBLICATIONS2020

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Fabio Nobile, Francesca Bonizzoni

We study the Darcy boundary value problem with lognormal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solut ...

2020

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