IEEE Transactions on Information Theory· 2013Q1
Compressed Sensing Off the Grid
- 1,174citations
- Q1SCImago
- 2013year
Short summary
A new atomic norm minimization approach recovers frequencies of complex sinusoids even when they are not restricted to a predefined grid, requiring only O(s log s log n) samples for s sinusoids and n total samples.
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Key points
- Introduces an atomic norm minimization approach for frequency estimation of complex sinusoids.
- Frequencies are not restricted to a grid, allowing estimation in a continuous [0, 1] domain.
- The method is reformulated as an exact semidefinite program.
- Guarantees exact frequency localization with high probability using O(s log s log n) samples for s sinusoids and n total samples, provided frequencies are well separated.
AI-generated from the title and abstract; the full text is not read.
Abstract
This paper investigates 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]. 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 O(slog s log n) 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 authors' abstract, as published at the source. IEEE Transactions on Information Theory, 2013 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering