Optimization methods for inverse problems

Nan Ye, Farbod Roosta-Khorasani, Tiangang Cui

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch

Abstract

Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging optimization problems. The inverse problem community has long been developing various techniques for solving such optimization tasks. However, other, seemingly disjoint communities, such as that of machine learning, have developed, almost in parallel, interesting alternative methods which might have stayed under the radar of the inverse problem community. In this survey, we aim to change that. In doing so, we first discuss current state-of-the-art optimization methods widely used in inverse problems. We then survey recent related advances in addressing similar challenges in problems faced by the machine learning community, and discuss their potential advantages for solving inverse problems. By highlighting the similarities among the optimization challenges faced by the inverse problem and the machine learning communities, we hope that this survey can serve as a bridge in bringing together these two communities and encourage cross fertilization of ideas.
Original languageEnglish
Title of host publication2017 MATRIX Annals
EditorsDavid R Wood, Jan de Gier, Cheryl E Praeger, Terence Tao
Place of PublicationCham Switzerland
PublisherSpringer
Chapter9
Pages121-140
Number of pages20
Volume2
ISBN (Electronic)9783030041618
ISBN (Print)9783030041601
DOIs
Publication statusPublished - 2019

Publication series

NameMATRIX Book Series
PublisherSpringer Nature Switzerland
Volume2
ISSN (Print)2523-3041
ISSN (Electronic)2523-305X

Cite this

Ye, N., Roosta-Khorasani, F., & Cui, T. (2019). Optimization methods for inverse problems. In D. R. Wood, J. de Gier, C. E. Praeger, & T. Tao (Eds.), 2017 MATRIX Annals (Vol. 2, pp. 121-140). (MATRIX Book Series; Vol. 2). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-030-04161-8_9