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Images Stacks as Parametric Surfaces (ISPS) is a powerful model that wasoriginally proposed for image registration. Being closely related to mutualinformation (MI) - the most classic similarity measure for image registration,ISPS works well across different categories of registration problems. TheSignals as Parametric Curves (SPC) model is derived from ISPS extended to1-dimensional signals. Blind Source Separation (BSS) is a classic problem insignal processing, where Independent Component Analysis (ICA) based approachesare popular and effective. Since MI plays an important role in ICA, based onthe close relationship with MI, we apply SPC model to BSS in this paper, andpropose a group of geometrical objective functions that are simple yetpowerful, and serve as replacements of original MI-based objective functions.Motivated by the geometrical objective functions, we also propose asecond-order-statistics approach, FT-PCA. Both geometrical objective functionsand FT-PCA consider signals as functions instead of stochastic processes, makeuse of derivative information of signals, and do not rely on the independenceassumption. In this paper, we discuss the reasonability of the assumptions ofgeometrical objective functions and FT-PCA, and show their effectiveness bysynthetic experiments, comparing with other previous classic approaches.

Signals as Parametric Curves: Application to Independent Component Analysis and Blind Source Separation