Theory of principal component filter banks with applications to multicomponent imagery

In the first part of the thesis we give background about the digital signal processing, required throughout. We introduce the Karhunen-Lo`eve transform and the most commonly used optimality criteria for orthonormal uniform filter banks. In the second part of the thesis the definition of principal component filter banks is given; these filter banks unify the theory of optimality of filter banks under explicitly stated criteria. We discuss the existence of principal component filter banks and present a study case pertaining to autoregressive input signals and finite impulse response filter banks. We prove a theorem on the existence of coding gain optimal finite impulse response filter banks. For filter banks with two channels, coding gain optimal filter banks are also principal component filter banks. As an application of the theory of optimal filter banks we design two-channel principal component filter banks for remote sensing hyper-spectral images. These filter banks are used to decorrelate an image, i.e. to represent the image in a more compact form. This design strategy leads do a more efficient compression of large images within the JPEG-2000 paradigm.