Concept

Well-posed problem

Related publications (77)

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

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

Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization

Isabel Haasler, Axel Ringh, Yiqiang Chen

In this letter we consider mean field type control problems with multiple species that have different dynamics. We formulate the discretized problem using a new type of entropy-regularized multimarginal optimal transport problems where the cost is a decomp ...

2023

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

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 rulesmust be known a priori or the system itself be accurately measured. The complexity of fullmeasurements of the system scales with its size. When exposed to real-wor ...

EPFL2022

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+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

Analysis of the flexible boundary condition method

William Curtin, Ankit Gupta

The flexible boundary condition method (FBCM) is a well-established method for the efficient study of complex non-linear atomistic defects while avoiding finite-size effects. The method uses lattice Green's functions (LGFs) to effectively embed an atomisti ...

IOP PUBLISHING LTD2021

Comparison of non-parametric T2 relaxometry methods for myelin water quantification

Jean-Philippe Thiran, Tobias Kober, Tom Hilbert, Erick Jorge Canales Rodriguez, Marco Pizzolato, Gian Franco Piredda, Thomas Yu, Alessandro Daducci, Nicolas Kunz

Multi-component T2 relaxometry allows probing tissue microstructure by assessing compartment-specific T2 relaxation times and water fractions, including the myelin water fraction. Non-negative least squares (NNLS) with zero-order Tikhonov regularization is ...

2021

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