Fundamentals of digital image processing
Fundamentals of digital image processing
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multirate systems and filter banks
Multirate systems and filter banks
Subband Image Coding
Introduction to Data Compression, Third Edition (Morgan Kaufmann Series in Multimedia Information and Systems)
Filterbank optimization with convex objectives and the optimalityof principal component forms
IEEE Transactions on Signal Processing
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Block Wavelet Transforms (BWTs) are orthogonal matrix transforms that can be obtained from orthogonal subband filter banks. They were initially generated to produce matrix transforms which may carry nice properties inheriting from wavelets, as alternatives to DCT and similarmatrix transforms. Although the construction methodology of BWT is clear, the reverse operation was not researched. In certain cases, a desirable matrix transform can be generated from available data using the Karhunen-Loéve transform (KLT). It is, therefore, of interest to develop a subband decomposition filter bank that leads to this particular KLT as its BWT. In this work, this dual problem is considered as a design attempt for the filter bank, hence the wavelets. The filters of the decomposition are obtained through lattice parameterization by minimizing the error between the KLT and the BWT matrices. The efficiency of the filters is measured according to the coding gains obtained after the subband decomposition and the experimental results are compared with Daubechies-2 and Daubechies-4 filter banks. It is shown that higher coding gains are obtained as the number of stages in the subband decomposition is increased.