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

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, to correct the skewness so that the filter responses can be described with a sum-of-Gaussians model. The correction enables us to use higher-order-moment information to analytically separate different source signal components. This provides us with an analytical framework to overcome the limited spectral resolution of other local spectral representations. Examples in source signal separation and local spectral multi-orientation analysis are shown.