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Gongguo Tang(gtang5wisc.edu) Abstract: We consider the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a grid, but can assume any values in the normalized frequency domain [0, 1]. We propose an atomic norm minimization approach to exactly recover the unobserved samples. We reformulate this atomic norm minimization as an exact semidefinite program. Even with this continuous dictionary, we show that most sampling sets of size O(s log s log n) are sufficient to guarantee the exact frequency estimation with high probability, provided the frequencies are well separated. Extensive numerical experiments are performed to illustrate the effectiveness of the proposed method. Keywords: atomic norm, basis mismatch, compressed sensing, continuous dictionary, line spectral estimation, nuclear norm relaxation, Prony’s method, sparsity Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Applications  Science and Engineering (DataMining ) Category 3: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Download: [PDF] Entry Submitted: 09/13/2012 Modify/Update this entry  
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