Using skew Gabor filter in source signal separation and local spectral orientation analysis

Authors:
Weichuan Yu;Gerald Sommer;Kostas Daniilidis;James S. Duncan
Affiliations:
Department of Diagnostic Radiology, Yale University BML 325, P.O. Box 208042, New Haven, CT 06520-8042, USA;Institute of Computer Science, Christian Albrechts University Preusserstrasse 1-9, D-24105 Kiel, Germany;GRASP Lab, University of Pennsylvania 3330 Walnut Street, Levine Hall, Philadelphia, PA 19104, USA;Department of Diagnostic Radiology and Electrical Engineering, Yale University BML 332, P.O. Box 208042, New Haven, CT 06520-8042, USA
Venue:
Image and Vision Computing
Year:
2005

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Abstract

Responses of Gabor wavelets in the mid-frequency space build a local spectral representation scheme with optimal properties regarding the time-frequency uncertainty principle. However, when using Gabor wavelets we observe a skewness in the mid-frequency space caused by the unsymmetrically spreading effect of Gabor wavelets. Though in most current applications the skewness does not obstruct the sampling of the spectral domain, it affects the identification and separation of source Signals from the filter response in the mid-frequency space. In this paper, we present a modification of the original Gabor filter, the skew Gabor filter, which corrects skewness so that the filter response can be described with a sum-of-Gaussians model in the mid-frequency space. The correction further enables us to use higher order moment information to analytically separate different source signal components. This provides us with an elegant framework to de-blur the filter response which is not characterized by the limited spectral resolution of other local spectral representations.