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On approximation of bandlimited functions with compressed sensing


Huber, Adrian E G; Liu, Shih-Chii (2018). On approximation of bandlimited functions with compressed sensing. In: 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada, 15 April 2018 - 20 April 2018.

Abstract

The application of Compressed Sensing techniques to bandlimited functions is investigated in this paper. It is shown that under the assumption of sparsity, stable reconstruction of a bandlimited function is possible from finitely many samples, contrary to classical results from signal processing theory. The number of measurements that need to be taken is proportional to the sparsity of the function. In compact intervals, it is shown that the number of pointwise measurements required scales quadratically with the size of the largest expansion coefficient (in a basis in which sparsity is measured) which is sufficient for a faithful function approximation.

Abstract

The application of Compressed Sensing techniques to bandlimited functions is investigated in this paper. It is shown that under the assumption of sparsity, stable reconstruction of a bandlimited function is possible from finitely many samples, contrary to classical results from signal processing theory. The number of measurements that need to be taken is proportional to the sparsity of the function. In compact intervals, it is shown that the number of pointwise measurements required scales quadratically with the size of the largest expansion coefficient (in a basis in which sparsity is measured) which is sufficient for a faithful function approximation.

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Additional indexing

Item Type:Conference or Workshop Item (Speech), not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Event End Date:20 April 2018
Deposited On:12 Mar 2019 13:18
Last Modified:17 Mar 2019 06:51
Publisher:IEEE
OA Status:Closed
Publisher DOI:https://doi.org/10.1109/ICASSP.2018.8461376

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