Sparse representations with minimum  norm
Proc. 50th Annual Allerton Conference on Communication
Overview
Maximum (or ) norm minimization subject to an
underdetermined system of linear equations finds use in a large
number of practical applications, such as vector quantization,
peak-to-average power ratio (PAPR) (or “crest factor”) reduction
in wireless communication systems, approximate neighbor search,
robotics, and control. In this paper, we analyze the fundamental
properties of signal representations with minimum -norm. In
particular, we develop bounds on the maximum magnitude of
such representations using the uncertainty principle (UP) introduced
by Lyubarskii and Vershynin, 2010, and we characterize
the limits of -norm-based PAPR reduction. Our results show
that matrices satisfying the UP, such as randomly subsampled
Fourier or i.i.d. Gaussian matrices, enable the efficient computation
of so-called democratic representations, which have both
provably small -norm and low PAPR.
Citation
C. Studer, W. Yin, and R.G. Baraniuk, Signal representations with minimum l_infity norm, in Proc. 50th Annual Allerton Conference on Communication, 2012.
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