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 the low-frequency band [-flo,flo] and seek to obtain a higher resolution estimate by extrapolating the spectrum up to a frequency fhi>flo. We show that as long as the sources are separated by 2/flo, 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) fhi/flo.
Original language | English (US) |
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Pages (from-to) | 1229-1254 |
Number of pages | 26 |
Journal | Journal of Fourier Analysis and Applications |
Volume | 19 |
Issue number | 6 |
DOIs | |
State | Published - Dec 2013 |
Keywords
- Basis mismatch
- Deconvolution
- Line spectra estimation
- Sparsity
- Stable signal recovery
- Super-resolution factor
ASJC Scopus subject areas
- Analysis
- Mathematics(all)
- Applied Mathematics