Publications associées à Problème bien posé

Aggregating Spatial and Photometric Context for Photometric Stereo

Photometric stereo, a computer vision technique for estimating the 3D shape of objects through images captured under varying illumination conditions, has been a topic of research for nearly four decades. In its general formulation, photometric stereo is an ...

EPFL2024

State of the Art in Dense Monocular Non-Rigid 3D Reconstruction

Pascal Fua

3D reconstruction of deformable (or non-rigid) scenes from a set of monocular 2D image observations is a long-standing and actively researched area of computer vision and graphics. It is an ill-posed inverse problem, since-without additional prior assumpti ...

WILEY2023

Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Michaël Unser, Thanh-An Michel Pham, Pakshal Narendra Bohra, Jonathan Yuelin Dong

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the im ...

2022

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

Farhad Rachidi-Haeri, Marcos Rubinstein

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

Learning of physical systems: from inference to control

Babak Rahmani

To characterize a physical system to behave as desired, either its underlying governing rules must be known a priori or the system itself be accurately measured. The complexity of full measurements of the system scales with its size. When exposed to real-w ...

EPFL2022

Learning to Represent and Reconstruct 3D Deformable Objects

Jan Bednarík

Representing and reconstructing 3D deformable shapes are two tightly linked problems that have long been studied within the computer vision field. Deformable shapes are truly ubiquitous in the real world, whether be it specific object classes such as human ...

EPFL2022

Ill-posedness of the quasilinear wave equation in the space 𝐻7/4(ln𝐻)−𝛽in ℝ2+1

Gaspard Ohlmann

We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...

EPFL2021

Learning Lipschitz-Controlled Activation Functions in Neural Networks for Plug-and-Play Image Reconstruction Methods

Michaël Unser, Dimitris Perdios, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sébastien Alexandre Emery

Ill-posed linear inverse problems are frequently encountered in image reconstruction tasks. Image reconstruction methods that combine the Plug-and-Play (PnP) priors framework with convolutional neural network (CNN) based denoisers have shown impressive per ...

2021

Benefiting From Bicubically Down-Sampled Images for Learning Real-World Image Super-Resolution

Jean-Philippe Thiran, Thomas Yu, Seyedbehzad Bozorgtabar, Claudiu-Cristian Musat, Hazim Kemal Ekenel, Mohammad Saeed Rad

Super-resolution (SR) has traditionally been based on pairs of high-resolution images (HR) and their low-resolution (LR) counterparts obtained artificially with bicubic downsampling. However, in real-world SR, there is a large variety of realistic image de ...

2021

Learning Self-Exciting Temporal Point Processes Under Noisy Observations

William Trouleau

Understanding the diffusion patterns of sequences of interdependent events is a central question for a variety of disciplines. Temporal point processes are a class of elegant and powerful models of such sequences; these processes have become popular across ...

EPFL2021