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Concept

Well-posed problem

Related publications (30)

Aggregating Spatial and Photometric Context for Photometric Stereo

David Honzátko

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, Alexis Marie Frederic Goujon, Pakshal Narendra Bohra

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

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

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

2020

Good Vibrations and Unknown Excitations

Dalia Salem Hassan Fahmy El Badawy

Inspired by the human ability to localize sounds, even with only one ear, as well as to recognize objects using active echolocation, we investigate the role of sound scattering and prior knowledge in regularizing ill-posed inverse problems in acoustics. In ...

EPFL2020

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Assyr Abdulle, Timothée Noé Pouchon

A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...

SPRINGER2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Deep-learning projector for optical diffraction tomography

Michaël Unser, Thanh-An Michel Pham, Harshit Gupta

Optical diffraction tomography is an effective tool to estimate the refractive indices of unknown objects. It proceeds by solving an ill-posed inverse problem for which the wave equation governs the scattering events. The solution has traditionally been de ...

2020

Consistency in Solving the Inverse Problem of the Voce-Chaboche Constitutive Model for Plastic Straining

Dimitrios Lignos, Albano António De Abreu E Presa De Castro E Sousa

This paper focuses on an inverse problem involving a commonly used material model in structural steel applications—the Voce-Chaboche model. In particular, the paper proposes an approach focused on obtaining a consistent set of material parameters that accu ...

2020

Point, Plane, Set, Match! Winning the Echo Grand SLAM

Miranda Krekovic

Some of the most important and challenging problems in science are inverse problems. They allow us to understand phenomena that cannot be measured directly. Inverse problems might not always have a unique or stable solution, or might not have any solution ...

EPFL2020

Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison

David Shuman

A major line of work in graph signal processing [2] during the past 10 years has been to design new transform methods that account for the underlying graph structure to identify and exploit structure in data residing on a connected, weighted, undirected gr ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Three-dimensional tomography of red blood cells using deep learning

Demetri Psaltis, Joowon Lim

We accurately reconstruct three-dimensional (3-D) refractive index (RI) distributions from highly ill-posed two-dimensional (2-D) measurements using a deep neural network (DNN). Strong distortions are introduced on reconstructions obtained by the Wolf tran ...

2020

Actor neural networks for the robust control of partially measured nonlinear systems showcased for image propagation through diffuse media

Demetri Psaltis, Christophe Moser, Damien Claude-Marie Loterie, Eirini Kakkava, Babak Rahmani, Ugur Tegin, Navid Borhani

The output of physical systems, such as the scrambled pattern formed by shining the spot of a laser pointer through fog, is often easily accessible by direct measurements. However, selection of the input of such a system to obtain a desired output is diffi ...

SPRINGERNATURE2020