TY - GEN
T1 - Maximal multiplicative spatial-spectral concentration on the sphere
T2 - 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
AU - Khalid, Zubair
AU - Kennedy, Rodney A.
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/8/4
Y1 - 2015/8/4
N2 - In this work, we design complete orthonormal basis functions, which are referred to as optimal basis functions, that span the vector sum of subspaces formed by band-limited spatially concentrated and space-limited spectrally concentrated functions. The optimal basis are shown to be a linear combination of band-limited functions with maximized energy concentration in some spatial region of interest and space-limited functions which maximize the energy concentration in some spectral region. The linear combination is designed with an optimality condition of maximizing the product of measures of energy concentration in the spatial and spectral domain. We also show that each optimal basis is an eigenfunction of a linear operator which maximizes the product of energy concentration measures in spatial and spectral domain. Finally, we discuss the properties of the proposed optimal basis functions and highlight their usefulness for the signal representation and data analysis due to the simultaneous concentration of the proposed basis functions in spatial and spectral domains.
AB - In this work, we design complete orthonormal basis functions, which are referred to as optimal basis functions, that span the vector sum of subspaces formed by band-limited spatially concentrated and space-limited spectrally concentrated functions. The optimal basis are shown to be a linear combination of band-limited functions with maximized energy concentration in some spatial region of interest and space-limited functions which maximize the energy concentration in some spectral region. The linear combination is designed with an optimality condition of maximizing the product of measures of energy concentration in the spatial and spectral domain. We also show that each optimal basis is an eigenfunction of a linear operator which maximizes the product of energy concentration measures in spatial and spectral domain. Finally, we discuss the properties of the proposed optimal basis functions and highlight their usefulness for the signal representation and data analysis due to the simultaneous concentration of the proposed basis functions in spatial and spectral domains.
KW - energy concentration problem
KW - localized spectral analysis
KW - spatial-spectral concentration
KW - unit sphere
UR - http://www.scopus.com/inward/record.url?scp=84946092135&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2015.7178754
DO - 10.1109/ICASSP.2015.7178754
M3 - Conference contribution
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4160
EP - 4164
BT - 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 19 April 2014 through 24 April 2014
ER -