Skewness of Gabor Wavelets and Source Signal Separation

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 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 separate different source signal components. This provides us with an elegant framework to deblur the filter response which is not characterized by the limited spectral resolution of other local spectral representations.