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COLT
2010
Springer

Deterministic Sparse Fourier Approximation via Fooling Arithmetic Progressions

11 years 7 months ago
Deterministic Sparse Fourier Approximation via Fooling Arithmetic Progressions
A significant Fourier transform (SFT) algorithm, given a threshold and oracle access to a function f, outputs (the frequencies and approximate values of) all the -significant Fourier coefficients of f, i.e., the Fourier coefficients whose magnitude exceeds f 2 2. In this paper we present the first deterministic SFT algorithm for functions f over ZN which is: (1) Local, i.e., its running time is polynomial in log N, 1/ and L1(f) (the L1 norm of f's Fourier transform). (2) Robust to random noise. This strictly extends the class of compressible/Fourier sparse functions over ZN efficiently handled by prior deterministic algorithms. As a corollary we obtain deterministic and robust algorithms for sparse Fourier approximation, compressed sensing and sketching. As a central tool, we prove that there are:
Adi Akavia
Added 10 Feb 2011
Updated 10 Feb 2011
Type Journal
Year 2010
Where COLT
Authors Adi Akavia
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