Nonuniform Nonunitary Perfect Reconstruction Filter Banks for Image Coding

Unitary and nonunitary lter banks with uniform frequency separation have been extensively studied in the past. Improvement in coding gain has been achieved when allowing for nonunitary lter banks in image coders. Subjective improvements can be achieved by employing nonuniform lter banks. The paper presents a method to construct nonuniform nonunitary perfect reconstruction lter banks. A polyphase matrix representation of nonuniform parallel lter banks is given for octave band splitting. In this case, results show that the parallel lter banks tend to become the tree-structured lter banks. It is further shown that the perfect reconstruction property can be met only by examining each stage of the tree-structured system in a polyphase matrix representation. Finally, frequency responses are presented when the lter banks are optimized for coding gain.