NDLI: A robust R-FFAST framework for computing a k-sparse n-length DFT in O(k log n) sample complexity using sparse-graph codes

Content Provider	IEEE Xplore Digital Library
Author	Pawar, S. Ramchandran, K.
Copyright Year	2014
Description	Author affiliation: Dept. of EECS, Univ. of California, Berkeley, Berkeley, CA, USA (Pawar, S.; Ramchandran, K.)
Abstract	The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X⃗ of the signal x⃗ has only k non-zero coefficients (where k <; n), can we do better? In [1], we presented a novel FFAST (Fast Fourier Aliasing-based Sparse Transform) algorithm that cleverly induces sparse graph codes in the DFT domain, via a Chinese-Remainder-Theorem (CRT)-guided sub-sampling operation of the time-domain samples. The resulting sparse graph code is then exploited to devise a simple and fast iterative onion-peeling style decoder that computes an n length DFT of a signal using only O(k) time-domain samples and O(k log k) computations, in the absence of any noise. In this paper, we extend the FFAST framework of [1] to the case where the time-domain samples are corrupted by white Gaussian noise. In particular, we show that the extended noise robust algorithm R-FFAST computes an n-length k-sparse DFT X⃗ using O(k log $n)^{1}$ noise-corrupted time-domain samples, in O(n log n) $computations^{2}.$ While our theoretical results are for signals with a uniformly random support of the non-zero DFT coefficients and additive white Gaussian noise, we provide simulation results which demonstrates that the R-FFAST algorithm performs well even for signals like MR images, that have an approximately sparse Fourier spectrum with a non-uniform support for the dominant DFT coefficients.
Starting Page	1852
Ending Page	1856
File Size	2619458
Page Count	5
File Format	PDF
ISBN	9781479951864
ISSN	21578117
DOI	10.1109/ISIT.2014.6875154
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Discrete Fourier transforms Time-domain analysis Noise Computer architecture Signal processing algorithms Vectors Information theory
Content Type	Text
Resource Type	Article

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