Super-Resolution from Noisy Data

By E.J. Candes, Carlos Fernandez-Granda. Journal of Fourier Analysis and Applications, 2012

419 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/b74aaba4afda839565732e4bc2e94242f912cea6

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In Biomedical Engineering

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Exact Support Recovery for Sparse Spikes Deconvolution (2013, positive): “…CF is not degenerate (i.e. ( η CF ) (cid:48)(cid:48) ( x i ) (cid:54) = 0 for all i = 1 , . . . , N ), the same authors derive an L 2 robustness to noise result in [7], and Fernandez-Granda and Azais et al. use the constructed certiﬁcate to analyze ﬁnely the local averages of the spikes in [19, 1].”
Direction of Arrival Estimation Using Co-Prime Arrays: A Super Resolution Viewpoint (2013, methodology): “We then consider the case which the number of time samples T is limited and demonstrate the robustness of super resolution via statistical analysis of the noise structure.”
Modern regularization methods for inverse problems (2018, background): “This yields a convex regularization functional for reconstructing multiple peaks at unknown locations and has been proposed for inverse problems in [56], respectively for superresolution problems in [100, 101, 3].”
On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data (2014, methodology): “Therefore, the atomic norm-based methods in [28] and later papers [31]–[33] correspond to gridless versions (or limiting scenarios with an inﬁnitely dense grid) of the (cid:96) 1 -based meth-ods.”