NDLI: On the use of singular value decomposition and decimation in discrete-time band-limited signal extrapolation

Content Provider	IEEE Xplore Digital Library
Author	Sullivan, B. Bede Liu
Copyright Year	1974
Abstract	The problem of extrapolating a band-limited signal in discrete time is viewed as one of solving an underdetermined system of linear equations. Choosing the minimum norm least-squares (MNLS) solution is one criterion for singling out an extrapolation from all the possible solutions to the linear system. Use of the Moore-Penrose inverse yields the MNLS solution, and singular value decomposition (SVD) provides a means for implementing the Moore-Penrose inverse. An expression for the mean-square error incurred in solving a linear system via SVD is derived. This can be used to estimate the number of singular values needed to form the inverse. The error expression also indicates that decimation can be applied in the extrapolation problem to reduce the high computational cost of SVD without degrading the extrapolation. The results developed for the one-dimensional case are extended to higher dimensions. Examples of the SVD approach to extrapolation are given, along with examples using other extrapolation techniques for comparison. The SVD approach compares favorably with known MNLS extrapolation methods.
Starting Page	1201
Ending Page	1212
Page Count	12
File Size	1020650
File Format	PDF
ISSN	00963518
Volume Number	32
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1984-12-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Singular value decomposition Extrapolation Equations Linear systems Signal analysis Optical signal processing Computational efficiency Degradation Image restoration
Content Type	Text
Resource Type	Article
Subject	Signal Processing

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in