Super-resolution in Phase Space
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Raskar_Super-resolution.pdf
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142.22 KB
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Author(s)
Bhandari, Ayush
Eldar, Yonina C.
Raskar, Ramesh
Date Issued
August 2015
Journal
2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Bhandari, Ayush, Yonina C. Eldar, and Ramesh Raskar. “Super-Resolution in Phase Space.” 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia, 19-24 April, 2015. IEEE, 2015, pp. 4155–4159.
Version
Author's final manuscript
Abstract
This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods. Recently, it has been shown that convex-optimization based formulations facilitate a continuous time solution to the super-resolution problem. Here we treat super-resolution from low-pass measurements in Phase Space. The Phase Space transformation parametrically generalizes a number of well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace and Fourier transforms. Consequently, our work provides a general super-resolution strategy which is backward compatible with the usual Fourier domain result. We consider low-pass measurements of Dirac distributions in Phase Space and show that the super-resolution problem can be cast as Total Variation minimization. Remarkably, even though are setting is quite general, the bounds on the minimum separation distance of Dirac distributions is comparable to existing methods.
MIT Department
Massachusetts Institute of Technology. Media Laboratory
Program in Media Arts and Sciences (Massachusetts Institute of Technology)
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/ICASSP.2015.7178753
