skip to main content
Guest
My Research
My Account
Sign out
Sign in
This feature requires javascript
Library Search
Find Databases
Browse Search
E-Journals A-Z
E-Books A-Z
Citation Linker
Help
Language:
English
Vietnamese
This feature required javascript
This feature requires javascript
Primo Search
All Library Resources
All
Course Materials
Course Materials
Search For:
Clear Search Box
Search in:
All Library Resources
Or hit Enter to replace search target
Or select another collection:
Search in:
All Library Resources
Search in:
Print Resources
Search in:
Digital Resources
Search in:
Online E-Resources
Advanced Search
Browse Search
This feature requires javascript
Search Limited to:
Search Limited to:
Resource type
criteria input
All items
Books
Articles
Images
Audio Visual
Maps
Graduate theses
Show Results with:
criteria input
that contain my query words
with my exact phrase
starts with
Show Results with:
Search type Index
criteria input
anywhere in the record
in the title
as author/creator
in subject
Full Text
ISBN
ISSN
TOC
Keyword
Field
Show Results with:
in the title
Show Results with:
anywhere in the record
in the title
as author/creator
in subject
Full Text
ISBN
ISSN
TOC
Keyword
Field
This feature requires javascript
The Convex Geometry of Linear Inverse Problems
Foundations of computational mathematics, 2012-12, Vol.12 (6), p.805-849
[Peer Reviewed Journal]
SFoCM 2012 ;COPYRIGHT 2012 Springer ;ISSN: 1615-3375 ;EISSN: 1615-3383 ;DOI: 10.1007/s10208-012-9135-7 ;CODEN: FCMOA3
Full text available
Citations
Cited by
View Online
Details
Recommendations
Reviews
Times Cited
External Links
This feature requires javascript
Actions
Add to My Research
Remove from My Research
E-mail
Print
Permalink
Citation
EasyBib
EndNote
RefWorks
Delicious
Export RIS
Export BibTeX
This feature requires javascript
Title:
The Convex Geometry of Linear Inverse Problems
Author:
Chandrasekaran, Venkat
;
Recht, Benjamin
;
Parrilo, Pablo A.
;
Willsky, Alan S.
Subjects:
Algebra
;
Applications of Mathematics
;
Atomic structure
;
Computational mathematics
;
Computer Science
;
Economics
;
Geometry
;
Inverse problems
;
Linear and Multilinear Algebras
;
Math Applications in Computer Science
;
Mathematical analysis
;
Mathematical models
;
Mathematics
;
Mathematics and Statistics
;
Matrices
;
Matrix methods
;
Matrix Theory
;
Norms
;
Numerical Analysis
;
Optimization
;
Programming
Is Part Of:
Foundations of computational mathematics, 2012-12, Vol.12 (6), p.805-849
Description:
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems. The class of simple models considered includes those formed as the sum of a few atoms from some (possibly infinite) elementary atomic set; examples include well-studied cases from many technical fields such as sparse vectors (signal processing, statistics) and low-rank matrices (control, statistics), as well as several others including sums of a few permutation matrices (ranked elections, multiobject tracking), low-rank tensors (computer vision, neuroscience), orthogonal matrices (machine learning), and atomic measures (system identification). The convex programming formulation is based on minimizing the norm induced by the convex hull of the atomic set; this norm is referred to as the atomic norm . The facial structure of the atomic norm ball carries a number of favorable properties that are useful for recovering simple models, and an analysis of the underlying convex geometry provides sharp estimates of the number of generic measurements required for exact and robust recovery of models from partial information. These estimates are based on computing the Gaussian widths of tangent cones to the atomic norm ball. When the atomic set has algebraic structure the resulting optimization problems can be solved or approximated via semidefinite programming. The quality of these approximations affects the number of measurements required for recovery, and this tradeoff is characterized via some examples. Thus this work extends the catalog of simple models (beyond sparse vectors and low-rank matrices) that can be recovered from limited linear information via tractable convex programming.
Publisher:
New York: Springer-Verlag
Language:
English
Identifier:
ISSN: 1615-3375
EISSN: 1615-3383
DOI: 10.1007/s10208-012-9135-7
CODEN: FCMOA3
Source:
Alma/SFX Local Collection
This feature requires javascript
This feature requires javascript
Back to results list
This feature requires javascript
This feature requires javascript
Searching Remote Databases, Please Wait
Searching for
in
scope:(TDTS),scope:(SFX),scope:(TDT),scope:(SEN),primo_central_multiple_fe
Show me what you have so far
This feature requires javascript
This feature requires javascript