Sampling from binary measurements - on reconstructions from Walsh coefficients
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Authors
Hansen, Anders
Terhaar, Laura
Publication Date
2017-07Journal Title
2017 International Conference on Sampling Theory and Applications (SampTA)
Publisher
IEEE
Type
Article
Metadata
Show full item recordCitation
Hansen, A., & Terhaar, L. (2017). Sampling from binary measurements - on reconstructions from Walsh coefficients. 2017 International Conference on Sampling Theory and Applications (SampTA) https://doi.org/10.1109/sampta.2017.8024449
Abstract
Reconstructing infinite-dimensional signals from a limited amount of linear measurements is a key problem in many applications such as medical imaging, single-pixel and lensless cameras, fluorescence microscopy etc. Efficient techniques for such a problem include generalized sampling and its compressed versions, as well as methods based on data assimilation. All of these methods have in common that the reconstruction quality depends highly on the subspace angle between the sampling and the reconstruction space. In this paper we consider the case of binary measurements, which, after a standard subtraction trick, can be converted to a 1 and -1 setup. These measurements are modelled with Walsh functions, which form the kernel for the Hadamard transform. For the reconstruction we use wavelets. We show that the relation between the amount of data sampled and the coefficients reconstructed has to be only linear to ensure that the angle is bounded from below and hence the reconstruction is accurate and stable.
Sponsorship
Engineering and Physical Sciences Research Council (EP/L016516/1)
Royal Society (UF160716)
Identifiers
External DOI: https://doi.org/10.1109/sampta.2017.8024449
This record's URL: https://www.repository.cam.ac.uk/handle/1810/282848
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http://www.rioxx.net/licenses/all-rights-reserved
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