Total Variation Reconstruction From Quasi-Random Samples

Colas Schretter; Ignace Loris; Ann Dooms; Peter Schelkens

Total Variation Reconstruction From Quasi-Random Samples

Colas Schretter, Ignace Loris, Ann Dooms, Peter Schelkens

Research output: Chapter in Book/Report/Conference proceeding › Conference paper

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Abstract

Pseudo-random numbers are often used for generating incoherent uniformly distributed sample distributions. However randomness is a sufficient -- not necessary -- condition to ensure incoherence. If one wants to reconstruct an image from few samples, choosing a globally optimized set of evenly distributed points could capture the visual content more efficiently. This work compares classical random sampling with a simple construction based on properties of the fractional Golden ratio sequence and the Hilbert space filling curve. Images are then reconstructed using a total variation prior. Results show improvements in terms of peak signal to noise ratio over pseudo-random sampling.

Original language	English
Title of host publication	iTWIST'14, international - Traveling Workshop on Interactions between Sparse models and Technology
Editors	Laurent Jacques
Pages	57-58
Publication status	Published - 2014
Event	iTWIST'14 international Traveling Workshop on Interactions between Sparse models and Technology - Namur, Belgium Duration: 27 Aug 2014 → 29 Aug 2014

Conference

Conference	iTWIST'14 international Traveling Workshop on Interactions between Sparse models and Technology
Country/Territory	Belgium
City	Namur
Period	27/08/14 → 29/08/14

Bibliographical note

Laurent Jacques

Keywords

Compressed sensing
Total variation

Access to Document

Schretter iTwist 2014Final published version, 1.68 MB

http://arxiv.org/abs/1410.0719

EU465: INTERFERE: Sparse Signal Coding for Interference-based Imaging Modalities
Schelkens, P. & Schelkens, P.
1/06/14 → 31/05/19
Project: Fundamental
SRP11: Strategic Research Programme: Processing of large scale multi-dimensional, multi-spectral, multi-sensorial and distributed data (M³D²)
Schelkens, P., Deligiannis, N., Jansen, B., Kuijk, M., Munteanu, A., Sahli, H., Steenhaut, K., Stiens, J., Schelkens, P., Cornelis, J. P., Kuijk, M., Munteanu, A., Sahli, H., Stiens, J. & Vounckx, R.
1/11/12 → 31/12/23
Project: Fundamental

Cite this

@inproceedings{89fea425a6de4788b8244cc87b1236d5,

title = "Total Variation Reconstruction From Quasi-Random Samples",

abstract = "Pseudo-random numbers are often used for generating incoherent uniformly distributed sample distributions. However randomness is a sufficient -- not necessary -- condition to ensure incoherence. If one wants to reconstruct an image from few samples, choosing a globally optimized set of evenly distributed points could capture the visual content more efficiently. This work compares classical random sampling with a simple construction based on properties of the fractional Golden ratio sequence and the Hilbert space filling curve. Images are then reconstructed using a total variation prior. Results show improvements in terms of peak signal to noise ratio over pseudo-random sampling.",

keywords = "Compressed sensing, Total variation",

author = "Colas Schretter and Ignace Loris and Ann Dooms and Peter Schelkens",

note = "Laurent Jacques; iTWIST'14 international Traveling Workshop on Interactions between Sparse models and Technology ; Conference date: 27-08-2014 Through 29-08-2014",

year = "2014",

language = "English",

pages = "57--58",

editor = "Laurent Jacques",

booktitle = "iTWIST'14, international - Traveling Workshop on Interactions between Sparse models and Technology",

}

Schretter, C, Loris, I, Dooms, A & Schelkens, P 2014, Total Variation Reconstruction From Quasi-Random Samples. in L Jacques (ed.), iTWIST'14, international - Traveling Workshop on Interactions between Sparse models and Technology. pp. 57-58, iTWIST'14 international Traveling Workshop on Interactions between Sparse models and Technology, Namur, Belgium, 27/08/14. <http://arxiv.org/abs/1410.0719>

TY - GEN

T1 - Total Variation Reconstruction From Quasi-Random Samples

AU - Schretter, Colas

AU - Loris, Ignace

AU - Dooms, Ann

AU - Schelkens, Peter

N1 - Laurent Jacques

PY - 2014

Y1 - 2014

N2 - Pseudo-random numbers are often used for generating incoherent uniformly distributed sample distributions. However randomness is a sufficient -- not necessary -- condition to ensure incoherence. If one wants to reconstruct an image from few samples, choosing a globally optimized set of evenly distributed points could capture the visual content more efficiently. This work compares classical random sampling with a simple construction based on properties of the fractional Golden ratio sequence and the Hilbert space filling curve. Images are then reconstructed using a total variation prior. Results show improvements in terms of peak signal to noise ratio over pseudo-random sampling.

AB - Pseudo-random numbers are often used for generating incoherent uniformly distributed sample distributions. However randomness is a sufficient -- not necessary -- condition to ensure incoherence. If one wants to reconstruct an image from few samples, choosing a globally optimized set of evenly distributed points could capture the visual content more efficiently. This work compares classical random sampling with a simple construction based on properties of the fractional Golden ratio sequence and the Hilbert space filling curve. Images are then reconstructed using a total variation prior. Results show improvements in terms of peak signal to noise ratio over pseudo-random sampling.

KW - Compressed sensing

KW - Total variation

M3 - Conference paper

SP - 57

EP - 58

BT - iTWIST'14, international - Traveling Workshop on Interactions between Sparse models and Technology

A2 - Jacques, Laurent

T2 - iTWIST'14 international Traveling Workshop on Interactions between Sparse models and Technology

Y2 - 27 August 2014 through 29 August 2014

ER -

Total Variation Reconstruction From Quasi-Random Samples

Abstract

Conference

Bibliographical note

Keywords

Access to Document

Fingerprint

Projects

EU465: INTERFERE: Sparse Signal Coding for Interference-based Imaging Modalities

SRP11: Strategic Research Programme: Processing of large scale multi-dimensional, multi-spectral, multi-sensorial and distributed data (M³D²)

Cite this