Conference proceeding
Sep]ration-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach
2018 IEEE International Symposium on Information Theory (ISIT), pp.76-80
06/2018
DOI: 10.1109/ISIT.2018.8437560
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.
Details
- Title: Subtitle
- Sep]ration-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach
- Creators
- Weiyu Xu - University of Iowa, Department of Electrical and Computer EngineeringJirong Yi - University of Iowa, Department of Electrical and Computer EngineeringSoura Dasgupta - University of Iowa, Department of Electrical and Computer EngineeringJian-Feng Cai - Hong Kong University of Science and Technology, Department of MathematicsMathews Jacob - University of Iowa, Department of Electrical and Computer EngineeringMyung Cho - University of Iowa, Department of Electrical and Computer Engineering
- Resource Type
- Conference proceeding
- Publication Details
- 2018 IEEE International Symposium on Information Theory (ISIT), pp.76-80
- DOI
- 10.1109/ISIT.2018.8437560
- eISSN
- 2157-8117
- Publisher
- IEEE
- Language
- English
- Date published
- 06/2018
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070437302771
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