This paper investigates the problem of estimating the frequency components of a mixture of complex sinusoids from a random subset of 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 . An atomic norm minimization approach is proposed to exactly recover the unobserved samples and identify the unknown frequencies, which is then reformulated as an exact semidefinite program. Even with this continuous dictionary, it is shown that random samples are sufficient to guarantee exact frequency localization with high probability, provided the frequencies are well separated. Extensive numerical experiments are performed to illustrate the effectiveness of the proposed method.
The problem of estimating frequencies in a mixture of sinusoids from noise-free compressive measurements is studied in REF .
Compressed Sensing Off the Grid
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics