A general framework is developed that combines semi-orthogonal transformation and reduced-rank filtering for noise reduction.
Under this new framework, several optimal reduced-rank filters are derived, including the maximum SNR, the Wiener, the tradeoff, and the MVDR filters.
Discussions are also provided on how to derive different semi-orthogonal transformations under four estimation criteria, including minimum correlation, minimum MSE, minimum distortion, and minimum residual noise.
Simulations are performed and the results show the properties of the deduced optimal reduced-rank filters.