@inproceedings{c697c76ecefc48809fae4fe12f7576ff,
title = "Signal analysis on the ball: Design of optimal basis functions with maximal multiplicative concentration in spatial and spectral domains",
abstract = "In this work, we design a set of complete orthonormal optimal basis functions for signals defined on the ball. We design the basis functions by maximizing the product of their energy concentration in some spatial region and that in some spectral region. The optimal basis functions are designed as a linear combination of space-limited functions with maximal concentration in the spectral region and band-limited functions with maximal concentration in the spatial region. The proposed optimal basis functions are shown to form a complete set for signal representation in a subspace formed by the vector sum of the subspaces spanned by space-limited and band-limited functions. We also formulate an integral operator which projects the signal to the joint subspace and maximizes the product of energy concentrations in harmonic and spatial domains. With the help of some properties of proposed optimal basis functions we show that these functions are the only eigenfunctions of the integral operator.",
keywords = "Slepian concentration problem, ball, energy concentration, localized spectral analysis, optimal basis, spatial-spectral concentration",
author = "Wajeeha Nafees and Zubair Khalid and Kennedy, {Rodney A.}",
note = "Publisher Copyright: {\textcopyright} 2017 IEEE.; 24th International Conference on Systems, Signals and Image Processing, IWSSIP 2017 ; Conference date: 22-05-2017 Through 24-05-2017",
year = "2017",
month = jun,
day = "30",
doi = "10.1109/IWSSIP.2017.7965574",
language = "English",
series = "International Conference on Systems, Signals, and Image Processing",
publisher = "IEEE Computer Society",
booktitle = "Proceedings - 2017 International Conference on Systems, Signals and Image Processing, IWSSIP 2017",
address = "United States",
}