Publications associées à Théorème de Radon

Deep Learning Meets Sparse Regularization

Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...

2023

Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

2023

An Inverse-Filter-Based Method to Locate Partial Discharge Sources in Power Transformers

Farhad Rachidi-Haeri, Marcos Rubinstein, Hamidreza Karami

Partial discharge (PD) occurrence in power transformers can lead to irreparable damage to the power network. In this paper, the inverse filter (IF) method to localize PDs in power transformers is proposed. To the best of the authors’ knowledge, this is the ...

2022

Piecewise linear interface-capturing volume-of-fluid method in axisymmetric cylindrical coordinates

Andreas Pautz, Lubomír Bures, Yohei Sato

The paper describes a novel implementation of the piecewise linear interface-capturing volume-of-fluid method (PLIC-VOF) in axisymmetric cylindrical coordinates. The principal innovative feature involved in this work is that both the forward and inverse re ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Methods and apparatus for three-dimensional fabrication by tomographic back projections

Christophe Moser, Paul Delrot, Damien Claude-Marie Loterie

A method for producing a three-dimensional object comprising computing a sequence of back-projections describing the three-dimensional object to be formed from different orientation angles of said object, defining a sequence of patterns of light using said ...

2019

Optical projection tomography for whole organ imaging

David Nguyen

In the past twenty years, far-reaching studies of molecular and cellular processes have reached a milestone in their maturation, and the knowledge from these studies was ready to apply at higher organizational levels. At that time, rodent models were long ...

EPFL2019

Imaging from Echoes: On Inverse Problems in Ultrasound

Adrien Georges Jean Besson

Ultrasound (US) imaging is currently living a revolution. On the one hand, ultrafast US imaging, a novel way of acquiring and producing US images, has paved the way to several advanced imaging modes, e.g. shear-wave elastography, ultrafast Doppler imaging ...

EPFL2018

Computational Super-Sectioning for Single-Slice Structured-Illumination Microscopy

Michaël Unser, Emmanuel Emilien Louis Soubies

While structured-illumination microscopy (SIM) is inherently a three-dimensional (3-D) technique, many biological questions can be addressed from the acquisition of a single focal plane with high lateral resolution. Unfortunately, the single-slice reconstr ...

2019

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Kyong Hwan Jin

Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

High-Quality Parallel-Ray x-Ray CT Back Projection Using Optimized Interpolation

Michaël Unser, Michael Thompson McCann

We propose a new, cost-efficient method for computing back projections in parallel-ray X-ray CT. Forward and back projections are the basis of almost all X-ray CT reconstruction methods, but computing these accurately is costly. In the special case of para ...

2017