Near-optimal sparse fourier representations via sampling

d Abstract] A. C. Gilbert S. Guhay P. Indykz S. Muthukrishnan M. Strauss We give an algorithm for nding a Fourier representation R of B terms for a given discrete signal A of length N, such that kA ; Rk2 2 is within the factor (1 + ) of best possible kA ; Roptk2 2. Our algorithm can access A by reading its values on a sample set T 0 N), chosen randomly from a (non-product) distribution of our choice, independent of A. That is, we sample non-adaptively. The total time cost of the algorithm is polynomial in Blog(N)log(M)= (where M is the ratio of largest to smallest numerical quantity encountered), which implies a similar bound for the number of samples.

• Type: Conference
• Year: 2002
• Where: STOC
• Authors: Anna C. Gilbert, Sudipto Guha, Piotr Indyk, S. Muthukrishnan, Martin Strauss
• Keywords: Algorithms, Guhay P, Smallest Numerical Quantity, STOC 2002, Total Time Cost