Imperial College London
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Dr. Ayush Bhandari

Faculty of Engineering, Department of Electrical and Electronic Engineering

Senior Lecturer
 
 
 
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Contact

 

+44 (0)20 7594 6233a.bhandari Website

 
 
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Location

 

802Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Bhandari:2019:10.1109/TSP.2018.2890064,
author = {Bhandari, A and Eldar, YC},
doi = {10.1109/TSP.2018.2890064},
journal = {IEEE Transactions on Signal Processing},
pages = {1508--1521},
title = {Sampling and super resolution of sparse signals beyond the Fourier domain},
url = {http://dx.doi.org/10.1109/TSP.2018.2890064},
volume = {67},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super resolution. In many cases, however, Fourier domain may not be the natural choice. For example, in holography, low-pass projections of sparse signals are obtained in the Fresnel domain. Similarly, time-varying system identification relies on low-pass projections on the space of linear frequency modulated signals. In this paper, we study the recovery of sparse signals from low-pass projections in the Special Affine Fourier Transform domain (SAFT). The SAFT parametrically generalizes a number of well-known unitary transformations that are used in signal processing and optics. In analogy to the Shannon's sampling framework, we specify sampling theorems for recovery of sparse signals considering three specific cases: 1) sampling with arbitrary, bandlimited kernels, 2) sampling with smooth, time-limited kernels, and 3) recovery from Gabor transform measurements linked with the SAFT domain. Our work offers a unifying perspective on the sparse sampling problem which is compatible with the Fourier, Fresnel, and Fractional Fourier domain-based results. In deriving our results, we introduce the SAFT series (analogous to the Fourier series) and the short-time SAFT, and study convolution theorems that establish a convolution-multiplication property in the SAFT domain.
AU  - Bhandari,A
AU  - Eldar,YC
DO  - 10.1109/TSP.2018.2890064
EP  - 1521
PY  - 2019///
SN  - 1053-587X
SP  - 1508
TI  - Sampling and super resolution of sparse signals beyond the Fourier domain
T2  - IEEE Transactions on Signal Processing
UR  - http://dx.doi.org/10.1109/TSP.2018.2890064
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000457991600002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/69477
VL  - 67
ER  -
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