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:

• Type: Journal
• Year: 2010
• Where: COLT
• Authors: Adi Akavia
• Keywords: Algorithms, COLT 2010, Deterministic, Fourier Coefficients, Machine Learning