Concept

Compact operator on Hilbert space

Publications associées (47)

Methodology And Convergence Rates For Functional Time Series Regression

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite-dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose inverse is by defi ...

STATISTICA SINICA2018

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Volkan Cevher, Junhong Lin

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...

2018

Region Of Interest X-Ray Computed Tomography Via Corrected Back Projection

Michaël Unser, Michael Thompson McCann, Laura Vilaclara

We present a new method for region of interest (ROI) reconstruction from high-resolution, nontruncated data in parallel-ray X-ray computed tomography (CT). Many of the approaches to ROI CT reconstruction in the literature rely on a costly forward projectio ...

IEEE2018

A Functional Framework for Enhanced Ultrasound Imaging

Ultrasound systems are cheap, portable, and fast, which have become impressively popular over the last decades. State-of art imaging is however known to be sub-optimal. Most attempts to improve it formulate the problem on a discrete spatial grid and suffer ...

2017

On the entropy of fermionic reduced density matrices

Marius Christopher Lemm

The antisymmetry of a fermionic quantum state has a marked effect on its entanglement properties. Recently, Carlen, Lieb and Reuvers (CLR) studied this effect, in particular concerning the entropy of the two-body reduced density matrix of a fermionic state ...

2017

Compact Side and Multi Angle Illumination Lensless Imager and Method of Operating the Same

Christophe Moser, Manon Rostykus

A system for subpixel resolution imaging of an amplitude and quantitative phase image, the system including a waveguide having a top plane, a bottom plane, and two sides, an array of light sources emitting first befit beams from one side of the two sides o ...

2017

Deep Convolutional Neural Network for Inverse Problems in Imaging

Michaël Unser, Kyong Hwan Jin, Michael Thompson McCann, Emmanuel Augustin Julien Froustey

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. ...

2017

A generalized mountain-pass theorem: the existence of multiple critical points

Hans-Jörg Ruppen

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

A Sound and Complete Axiomatization of Majority-n Logic

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù, Anupam Chattopadhyay

Manipulating logic functions via majority operators recently drew the attention of researchers in computer science. For example, circuit optimization based on majority operators enables superior results as compared to traditional logic systems. Also, the B ...

Institute of Electrical and Electronics Engineers2016

Estimation in Functional Lagged Regression

Lukasz Kidzinski

The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...

Wiley-Blackwell2015

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