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arXiv · 1506.03144

Superresolution without Separation

Geoffrey Schiebinger·Elina Robeva·Benjamin Recht
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Abstract

This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of M shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from 2M + 1 observations. This recovery is achieved by solving a a weighted version of basis pursuit over a continuous dictionary. Our methods combine classical polynomial interpolation techniques with contemporary tools from compressed sensing.

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Geoffrey Schiebinger, Elina Robeva, Benjamin Recht. 2015-06-10. Superresolution without Separation. https://arxiv.org/abs/1506.03144

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