Tutorial: Sparse Recovery Using Sparse Matrices - People.csail.mit.edu
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Tutorial: Sparse Recovery Using Sparse Matrices - People.csail.mit.edu
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Tutorial: Sparse Recovery Using Sparse Matrices Piotr Indyk MIT
Problem Formulation •
(approximation theory, learning Fourier coeffs, linear sketching, finite rate of innovation, compressed sensing...)
Setup:
– Data/signal in n-dimensional space : x E.g., x is an 256x256 image ⇒ n=65536 – Goal: compress x into a “sketch” Ax , where A is a m x n “sketch matrix”, m 1/2 • Assume |xi1| ≥ … ≥ |xim| and let S={i1…ik} (“elephants”) • When is xi* > xi ± α Err/k ? – Event 1: S and i collide, i.e., h(i) in h(S-{i}) Probability: at most k/(4/α)k = α/4
