Super-Resolution from Noisy Data

Emmanuel Candes; Carlos Fernandez-Granda

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arXiv · 1211.0290

Super-Resolution from Noisy Data

Emmanuel Candes·Carlos Fernandez-Granda

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Abstract

This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off frequency and seek to obtain a higher resolution estimate by extrapolating the spectrum up to a higher frequency. We show that as long as the sources are separated by twice the inverse of the cut-off frequency, solving a simple convex program produces a stable estimate in the sense that the approximation error between the higher-resolution reconstruction and the truth is proportional to the noise level times the square of the super-resolution factor (SRF), which is the ratio between the desired high frequency and the cut-off frequency of the data.

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BibTeX RIS

Emmanuel Candes, Carlos Fernandez-Granda. 2012-11-01. Super-Resolution from Noisy Data. https://arxiv.org/abs/1211.0290

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