Paper Info
Title
Sep]ration-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach.
Abstract
We consider the problem of recovering the superposition of $R$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the literature to recover the $R$ frequencies or the missing data. However, in order for TV minimization and atomic norm minimization to recover the missing data or the frequencies, the underlying $R$ frequencies are required to be well-separated, even when the measurements are noiseless. This paper shows that the Hankel matrix recovery approach can super-resolve the $R$ complex exponentials and their frequencies from compressed nonuniform measurements, regardless of how close their frequencies are to each other. We propose a new concept of orthonormal atomic norm minimization (OANM), and demonstrate that the success of Hankel matrix recovery in separation-free super-resolution comes from the fact that the nuclear norm of a Hankel matrix is an orthonormal atomic norm. More specifically, we show that, in traditional atomic norm minimization, the underlying parameter values must be well separated to achieve successful signal recovery, if the atoms are changing continuously with respect to the continuously-valued parameter. In contrast, for the OANM, it is possible the OANM is successful even though the original atoms can be arbitrarily close.
Year
DOI
Venue
2018
10.1109/isit.2018.8437560
ISIT
Field
DocType
Citations 
Mathematical optimization,Superposition principle,Exponential function,Mathematical analysis,Matrix norm,Euler's formula,Minification,Orthonormal basis,Hankel matrix,Mathematics,Compressed sensing
Conference
0
PageRank 
References 
Authors
0.34
0
6
Name
Order
Citations
PageRank
Weiyu Xu156354.45
Jirong Yi200.34
Soura Dasgupta367996.96
Jian-Feng Cai42828125.44
Mathews Jacob579059.62
Myung Cho6458.89