École Polytechnique Fédérale de Lausanne

About: École Polytechnique Fédérale de Lausanne is a facility organization based out in Lausanne, Switzerland. It is known for research contribution in the topics: Population & Catalysis. The organization has 44041 authors who have published 98296 publications receiving 4372092 citations. The organization is also known as: EPFL & ETHL.

Deep Convolutional Neural Network for Inverse Problems in Imaging

Abstract: In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise non-linearity) when the normal operator ( $H^{*}H$ , where $H^{*}$ is the adjoint of the forward imaging operator, $H$ ) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a $512\times 512$ image on the GPU.

Semidefinite programming relaxations for semialgebraic problems

Abstract: A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials, and some results from real algebraic geometry. The techniques provide a constructive approach for finding bounded degree solutions to the Positivstellensatz, and are illustrated with examples from diverse application fields.

Curling and closure of graphitic networks under electron-beam irradiation

Abstract: THE discovery1 of buckminsterfullerene (C60) and its production in macroscopic quantities2 has stimulated a great deal of research. More recently, attention has turned towards other curved graphitic networks, such as the giant fullerenes (Cn, n > 100)3,4 and carbon nanotubes5–8. A general mechanism has been proposed9 in which the graphitic sheets bend in an attempt to eliminate the highly energetic dangling bonds present at the edge of the growing structure. Here, I report the response of carbon soot particles and tubular graphitic structures to intense electron-beam irradiation in a high-resolution electron microscope; such conditions resemble a high-temperature regime, permitting a degree of structural fluidity. With increased irradiation, there is a gradual reorganization of the initial material into quasi-spherical particles composed of concentric graphitic shells. This lends weight to the nucleation scheme proposed9 for fullerenes, and moreover, suggests that planar graphite may not be the most stable allotrope of carbon in systems of limited size.