Optimal fixed rank transform of the second degree

We present a new technique with potential applications to numerous areas in signal processing including data compression, filtering, blind channel equalization, and feature selection and classification in pattern recognition. The technique is based on the best constrained approximation of a stochastic signal by a specific second degree operator acting on the noisy observed data and therefore is called the second degree transform. The proposed transform generalizes an approach by Hua and Liu (1998) and gives a better performance in comparison. This paper provides a strict justification of the technique proposed and shows its useful application to data compression and filtering.