Hybrid compressive sampling via a new total variation TVL1

Xianbiao Shu, Narendra Ahuja

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

Abstract

Compressive sampling (CS) is aimed at acquiring a signal or image from data which is deemed insufficient by Nyquist/Shannon sampling theorem. Its main idea is to recover a signal from limited measurements by exploring the prior knowledge that the signal is sparse or compressible in some domain. In this paper, we propose a CS approach using a new total-variation measure TVL1, or equivalently TVℓ1, which enforces the sparsity and the directional continuity in the gradient domain. Our TVℓ1 based CS is characterized by the following attributes. First, by minimizing the ℓ1-norm of partial gradients, it can achieve greater accuracy than the widely-used TVℓ1ℓ2 based CS. Second, it, named hybrid CS, combines low-resolution sampling (LRS) and random sampling (RS), which is motivated by our induction that these two sampling methods are complementary. Finally, our theoretical and experimental results demonstrate that our hybrid CS using TVℓ1 yields sharper and more accurate images.

Original languageEnglish (US)
Title of host publicationComputer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings
PublisherSpringer-Verlag
Pages393-404
Number of pages12
EditionPART 6
ISBN (Print)3642155669, 9783642155666
DOIs
StatePublished - Jan 1 2010
Event11th European Conference on Computer Vision, ECCV 2010 - Heraklion, Crete, Greece
Duration: Sep 10 2010Sep 11 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 6
Volume6316 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th European Conference on Computer Vision, ECCV 2010
CountryGreece
CityHeraklion, Crete
Period9/10/109/11/10

Fingerprint

Total Variation
Sampling
Gradient
Sampling Theorem
Random Sampling
Sampling Methods
Sparsity
Prior Knowledge
Proof by induction
Attribute
Norm
Partial
Experimental Results
Demonstrate

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Shu, X., & Ahuja, N. (2010). Hybrid compressive sampling via a new total variation TVL1. In Computer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings (PART 6 ed., pp. 393-404). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6316 LNCS, No. PART 6). Springer-Verlag. https://doi.org/10.1007/978-3-642-15567-3_29

Hybrid compressive sampling via a new total variation TVL1. / Shu, Xianbiao; Ahuja, Narendra.

Computer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings. PART 6. ed. Springer-Verlag, 2010. p. 393-404 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6316 LNCS, No. PART 6).

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

Shu, X & Ahuja, N 2010, Hybrid compressive sampling via a new total variation TVL1. in Computer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings. PART 6 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 6, vol. 6316 LNCS, Springer-Verlag, pp. 393-404, 11th European Conference on Computer Vision, ECCV 2010, Heraklion, Crete, Greece, 9/10/10. https://doi.org/10.1007/978-3-642-15567-3_29
Shu X, Ahuja N. Hybrid compressive sampling via a new total variation TVL1. In Computer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings. PART 6 ed. Springer-Verlag. 2010. p. 393-404. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 6). https://doi.org/10.1007/978-3-642-15567-3_29
Shu, Xianbiao ; Ahuja, Narendra. / Hybrid compressive sampling via a new total variation TVL1. Computer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings. PART 6. ed. Springer-Verlag, 2010. pp. 393-404 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 6).
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