On the stable sampling rate for binary measurements and wavelet reconstruction
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Authors
Thesing, L
Hansen, Anders Christian
Publication Date
2020Journal Title
Applied and Computational Harmonic Analysis
ISSN
1096-603X
Publisher
Elsevier
Type
Article
Metadata
Show full item recordCitation
Thesing, L., & Hansen, A. C. (2020). On the stable sampling rate for binary measurements and wavelet reconstruction. Applied and Computational Harmonic Analysis https://doi.org/10.1016/j.acha.2018.08.004
Abstract
This paper is concerned with the problem of reconstructing an infinite-dimensional signal from a limited number of linear measurements. In particular, we show that for binary measurements (modelled with
Walsh functions and Hadamard matrices) and wavelet reconstruction the stable sampling rate is linear. This implies that binary measurements are as efficient as Fourier samples when using wavelets as the reconstruction space. Powerful techniques for reconstructions include generalized sampling and its compressed versions, as well as recent methods based on data assimilation. Common to these methods is that the reconstruction quality depends highly on the subspace angle between the sampling and the reconstruction space, which is dictated by
the stable sampling rate. As a result of the theory provided in this paper, these methods can now easily use binary measurements and wavelet reconstruction bases.
Keywords
sampling theory, generalized sampling, wavelets, Walsh functions, stable sampling rate, data assimilation, Hilbert spaces
Sponsorship
This work of LT was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis. ACH acknowledges support from Royal Society University Research Fellowship as well as the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L003457/1.
Funder references
Engineering and Physical Sciences Research Council (EP/L016516/1)
Engineering and Physical Sciences Research Council (EP/L003457/1)
Royal Society (UF160716)
Identifiers
External DOI: https://doi.org/10.1016/j.acha.2018.08.004
This record's URL: https://www.repository.cam.ac.uk/handle/1810/282849
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
Licence:
http://creativecommons.org/licenses/by-nc-nd/4.0/
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