Exploiting residual information in the parameter choice for discrete ill-posed problems

Publication: Research - peer-reviewJournal article – Annual report year: 2006

View graph of relations

Most algorithms for choosing the regularization parameter in a discrete ill-posed problem are based on the norm of the residual vector. In this work we propose a different approach, where we seek to use all the information available in the residual vector. We present important relations between the residual components and the amount of information that is available in the noisy data, and we show how to use statistical tools and fast Fourier transforms to extract this information efficiently. This approach leads to a computationally inexpensive parameter-choice rule based on the normalized cumulative periodogram, which is particularly suited for large-scale problems.
Original languageEnglish
JournalBIT Numerical Mathematics
Publication date2006
Volume46
Issue1
Pages41-59
ISSN0006-3835
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 30
Download as:
Download as PDF
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
PDF
Download as HTML
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
HTML
Download as Word
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
Word

ID: 2926149