NDLI: A Robust Sparse Fourier Transform in the Continuous Setting

Content Provider	IEEE Xplore Digital Library
Author	Price, E. Zhao Song
Copyright Year	2015
Description	Author affiliation: Dept. of Comput. Sci., Univ. of Texas at Austin, Austin, TX, USA (Price, E.; Zhao Song)
Abstract	In recent years, a number of works have studied methods for computing the Fourier transform in sublinear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is continuous and naive discretization significantly worsens the sparsity level. We present an algorithm for robustly computing sparse Fourier transforms in the continuous setting. Let x(t) = x(t)+g(t), where x has a k-sparse Fourier transform and g is an arbitrary noise term. Given sample access to x(t) for some duration T, we show how to find a k-Fourier-sparse reconstruction x'(t) with 1/T $∫_{0}^{T}\|x'(t)$ - $x(t)\|^{2}dt$ ≲ $1/T∫_{0}^{T}\|g(t)\|^{2}dt.$ The sample complexity is linear in k and logarithmic in the signal-to-noise ratio and the frequency resolution. Previous results with similar sample complexities could not tolerate an infinitesimal amount of i.i.d. Gaussian noise, and even algorithms with higher sample complexities increased the noise by a polynomial factor. We also give new results for how precisely the individual frequencies of x* can be recovered.
Starting Page	583
Ending Page	600
File Size	366507
Page Count	18
File Format	PDF
ISBN	9781467381918
ISSN	02725428
DOI	10.1109/FOCS.2015.42
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-10-17
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fourier transforms Robustness Complexity theory Signal to noise ratio Approximation algorithms Signal resolution Standards Superresolution Fourier Transform Sparse Recovery
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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