Sampling from binary measurements - on reconstructions from Walsh coefficients

Authors
Hansen, Anders 
Terhaar, Laura 

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Article
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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.

Publication Date
2017-07
Online Publication Date
Acceptance Date
2017-04-03
Keywords
46 Information and Computing Sciences, 4006 Communications Engineering, 40 Engineering, 4603 Computer Vision and Multimedia Computation
Journal Title
2017 International Conference on Sampling Theory and Applications (SampTA)
Journal ISSN
Volume Title
Publisher
IEEE
Sponsorship
Engineering and Physical Sciences Research Council (EP/L016516/1)
Royal Society (UF160716)