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.
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>
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) http://arxiv.org/abs/1410.0719
@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",
}