Concept

Inverse problem

Related publications (32)

On the reconstruction of the attenuation function of a return-stroke current from the Fourier Transform of finite-duration measurements

A correct representation of the lightning current is crucial when the electromagnetic field radiated to a point of interest has to be computed. Based on the engineering models of Transmission Line type, such representation involves the knowledge of the ret ...

2022

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

Alfio Quarteroni, Simone Deparis, Stefano Pagani, Riccardo Tenderini

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...

2022

HIERARCHICAL MARKOV CHAIN MONTE CARLO METHODS FOR BAYESIAN INVERSE PROBLEMS

Juan Pablo Madrigal Cianci

This thesis is devoted to the construction, analysis, and implementation of two types of hierarchical Markov Chain Monte Carlo (MCMC) methods for the solution of large-scale Bayesian Inverse Problems (BIP). The first hierarchical method we present is base ...

EPFL2022

Physics-informed neural networks for diffraction tomography

Demetri Psaltis, Carlo Gigli, Amirhossein Saba Shirvan

We propose a physics-informed neural network (PINN) as the forward model for tomographic reconstructions of biological samples. We demonstrate that by training this network with the Helmholtz equation as a physical loss, we can predict the scattered field ...

SPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERS2022

Validation of a Non-invasive Inverse Problem-Solving Method for Stroke Volume

Nikolaos Stergiopoulos, Vasiliki Bikia, Georgios Rovas, Stamatia Zoi Pagoulatou

Stroke volume (SV) is a major biomarker of cardiac function, reflecting ventricular-vascular coupling. Despite this, hemodynamic monitoring and management seldomly includes assessments of SV and remains predominantly guided by brachial cuff blood pressure ...

FRONTIERS MEDIA SA2022

Differentiable Physically Based Rendering: Algorithms, Systems and Applications

Merlin Eléazar Nimier-David

Physically based rendering methods can create photorealistic images by simulating the propagation and interaction of light in a virtual scene. Given a scene description including the shape of objects, participating media, material properties, etc., the sim ...

EPFL2022

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

Learning with tensors: a framework based on convex optimization and spectral regularization

Quoc Tran Dinh

We present a framework based on convex optimization and spectral regularization to perform learning when feature observations are multidimensional arrays (tensors). We give a mathematical characterization of spectral penalties for tensors and analyze a uni ...

Springer2014

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Robust, High-Speed Interest Point Matching for Real-Time Applications

Michael Calonder

A typical Computer Vision system needs to process vast amounts of data as captured by one or more cameras, constantly testing the capabilities of today's hardware. Yet such systems face an ever-growing computational load caused by the more and more demandi ...

EPFL2010

Learning to sample in Cartesian MRI

Thomas Sanchez

Magnetic Resonance Imaging (MRI) is a non-invasive, non-ionizing imaging modality with unmatched soft tissue contrast. However, compared to imaging methods like X-ray radiography, MRI suffers from long scanning times, due to its inherently sequential acqui ...

EPFL2022

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