On the effective measure of dimension in total variation minimization

Raja Giryes, Yaniv Plan, Roman Vershynin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Total variation (TV) is a widely used technique in many signal and image processing applications. One of the famous TV based algorithms is TV denoising that performs well with piecewise constant images. The same prior has been used also in the context of compressed sensing for recovering a signal from a small number of measurements. Recently, it has been shown that the number of measurements needed for such a recovery is proportional to the size of the edges in the sampled image and not the number of connected components in the image. In this work we show that this is not a coincidence and that the number of connected components in a piecewise constant image cannot serve alone as a measure for the complexity of the image. Our result is not limited only to images but holds also for higher dimensional signals. We believe that the results in this work provide a better insight into the TV prior.

Original languageEnglish
Title of host publication2015 International Conference on Sampling Theory and Applications, SampTA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages593-597
Number of pages5
ISBN (Electronic)9781467373531
DOIs
StatePublished - 2 Jul 2015
Externally publishedYes
Event11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States
Duration: 25 May 201529 May 2015

Publication series

Name2015 International Conference on Sampling Theory and Applications, SampTA 2015

Conference

Conference11th International Conference on Sampling Theory and Applications, SampTA 2015
Country/TerritoryUnited States
CityWashington
Period25/05/1529/05/15

Fingerprint

Dive into the research topics of 'On the effective measure of dimension in total variation minimization'. Together they form a unique fingerprint.

Cite this