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In recent years, a number of works have studied methods for computing the Fourier transform in sublinear time if the output is sparse.
An algorithm for the machine calculation of complex Fourier series
James W Cooley and John W Tukey · 1965
Earlier work this paper cites.
Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise
Yingbo Hua and Tapan K Sarkar · 1990
Earlier work this paper cites.
Finding frequent items in data streams
Moses Charikar, Kevin Chen, and Martin Farach-Colton · 2002
Earlier work this paper cites.
Near-optimal sparse Fourier representations via sampling
Anna C Gilbert, Sudipto Guha, Piotr Indyk, S Muthukrishnan, and Martin Strauss · 2002
Earlier work this paper cites.
Improved time bounds for near-optimal sparse Fourier representations
Anna C Gilbert, S Muthukrishnan, and Martin Strauss · 2005
Earlier work this paper cites.
Approximate sparse recovery: optimizing time and measurements
Anna C Gilbert, Yi Li, Ely Porat, and Martin J Strauss · 2012
Earlier work this paper cites.
Nearly optimal sparse Fourier transform
Haitham Hassanieh, Piotr Indyk, Dina Katabi, and Eric Price · 2012
Cited alongside, same era.
Simple and practical algorithm for sparse Fourier transform
Haitham Hassanieh, Piotr Indyk, Dina Katabi, and Eric Price · 2012
Cited alongside, same era.
Spectral compressive sensing
Marco F Duarte and Richard G Baraniuk · 2013
Cited alongside, same era.
Mrs sparse-fft: Reducing acquisition time and artifacts for in vivo 2d correlation spectroscopy
Lixin Shi, O Andronesi, Haitham Hassanieh, Badih Ghazi, Dina Katabi, and Elfar Adalsteinsson · 2013
Cited alongside, same era.
Compressed sensing off the grid
Gongguo Tang, Badri Narayan Bhaskar, Parikshit Shah, and Benjamin Recht · 2013
Cited alongside, same era.
What’s the frequency, Kenneth?: Sublinear Fourier sampling off the grid
Petros Boufounos, Volkan Cevher, Anna C Gilbert, Yi Li, and Martin J Strauss · 2014
Towards a mathematical theory of super-resolution
Emmanuel J Candès and Carlos Fernandez-Granda · 2014
Later among the works it cites.
Sample-optimal Fourier sampling in any constant dimension
Piotr Indyk and Michael Kapralov · 2014
Later among the works it cites.
(Nearly) Sample-optimal sparse Fourier transform
Piotr Indyk, Michael Kapralov, and Eric Price · 2014
Later among the works it cites.
The threshold for super-resolution via extremal functions
Ankur Moitra · 2015
Later among the works it cites.
Achieving high resolution for super-resolution via reweighted atomic norm minimization
Zai Yang and Lihua Xie · 2015
Later among the works it cites.
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Cited alongside, same era.