Sample-Optimal Fourier Sampling in Any Constant Dimension
Author(s)Indyk, Piotr; Kapralov, Mikhail
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We give an algorithm for ℓ[subscript 2]/ℓ[subscript 2] sparse recovery from Fourier measurements using O(k log N) samples, matching the lower bound of Do Ba-Indyk-Price-Woodruff'10 for non-adaptive algorithms up to constant factors for any k ≤ N [superscript 1-δ]. The algorithm runs in Õ(N) time. Our algorithm extends to higher dimensions, leading to sample complexity of Õd(k log N), which is optimal up to constant factors for any d = O(1). These are the first sample optimal algorithms for these problems. A preliminary experimental evaluation indicates that our algorithm has empirical sampling complexity comparable to that of other recovery methods known in the literature, while providing strong provable guarantees on the recovery quality.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
Institute of Electrical and Electronics Engineers (IEEE)
Indyk, Piotr, and Kapralov, Michael. “Sample-Optimal Fourier Sampling in Any Constant Dimension.” 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, Philadelphia, Pennsylvania, USA, October 18-21 2014, Institute of Electrical and Electronics Engineers (IEEE), December 2014