Applications
Triple correlation methods are frequently used in signal processing for treating signals that are corrupted by additive white Gaussian noise; in particular, triple correlation techniques are suitable when multiple observations of the signal are available and the signal may be translating in between the observations, e.g.,a sequence of images of an object translating on a noisy background. What makes the triple correlation particularly useful for such tasks are three properties: (1) it is invariant under translation of the underlying signal; (2) it is unbiased in additive Gaussian noise; and (3) it retains nearly all of the relevant phase information in the underlying signal. Properties (1)-(3) of the triple correlation extend in many cases to functions on an arbitrary locally compact group, in particular to the groups of rotations and rigid motions of euclidean space that arise in computer vision and signal processing.
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