Solving inverse problems using data-driven models

被引：363

作者：

Arridge, Simon ^{[1
]}

Maass, Peter ^{[2
]}

Oktem, Ozan ^{[3
]}

Schonlieb, Carola-Bibiane ^{[4
]}

机构：

[1] UCL, Dept Comp Sci, Gower St, London WC1E 6BT, England

[2] Univ Bremen, Dept Math, Postfach 330 440, D-28344 Bremen, Germany

[3] KTH Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden

[4] Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

来源：

ACTA NUMERICA | 2019年 / 28卷

基金：

英国工程与自然科学研究理事会;

关键词：

LOW-DOSE CT; CONVOLUTIONAL NEURAL-NETWORKS; ILL-POSED PROBLEMS; GENERATIVE ADVERSARIAL NETWORK; POSTERIOR CONTRACTION RATES; IMAGE-RESTORATION; CONVERGENCE-RATES; SIGNAL RECOVERY; REGULARIZATION METHODS; TIKHONOV REGULARIZATION;

D O I：

10.1017/S0962492919000059

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical-analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

引用

页码：1 / 174

页数：174

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