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Support adaptive hermite-Gaussian expansion for analysis of multi-component signals

For a signal component whose time-frequency support tightly fits into a circular region around origin, Hermite-Gaussian function expansion provides optimal representation by using the fewest number of basis functions. However, for signal components which have non-circular time-frequency supports away from the origin, straight forward expansions require excessively large number of Hermite-Gaussians which result in unreliable component estimates especially when the available observation is noisy or includes multiple components. To alleviate this problem, we propose a fully automated pre-processing technique which identifies and transforms supports of individual signal components to a circular region centered around origin so that the fewest number of Hermite-Gaussians can be used for obtaining reliable component estimates. Then, estimated components are post-processed to transform their supports back to their original positions.