| In the first part of the thesis we give background about the digital signal processing, required throughout. We introduce the Karhunen-Loève 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. |
