Group-theoretic structure of linear phase multirate filter banks

Unique lifting factorization results for group lifting structures are used to characterize the group-theoretic structure of two-channel linear phase FIR perfect reconstruction filter bank groups. For D-invariant, order-increasing group lifting structures, it is shown that the associated lifting cascade group C is isomorphic to the free product of the upper and lower triangular lifting matrix groups. Under the same hypotheses, the associated scaled lifting group S is the semidirect product of C by the diagonal gain scaling matrix group D. These results apply to the group lifting structures for the two principal classes of linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Since the unimodular whole-sample symmetric class forms a group, W, that is in fact equal to its own scaled lifting group, W=S_W, the results of this paper characterize the group-theoretic structure of W up to isomorphism. Although the half-sample symmetric class H does not form a group, it can be partitioned into cosets of its lifting cascade group, C_H, or, alternatively, into cosets of its scaled lifting group, S_H. Homomorphic comparisons reveal that scaled lifting groups covered by the results in this paper have a structure analogous to a "noncommutative vector space."Comment: 33 pages, 6 figures; to appear in IEEE Transactions on Information Theor

Image coding for digitized libraries

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1998.Thesis (Ph.D.) -- Bilkent University, 1998.Includes bibliographical references leaves 104-113III this thesis, image coding methods for two basic image types are developed under a digitized library framework. The two image types are gray tone or color images, and binary textual images, which are the digitized image versions of text documents. The grciy tone images are encoded using an adaptive subband decomposition followed by zerotree quantizers. The adaptive sub- l)and decomposition filter bank adaptively updates the filter bank coefficients in which the values of one of the subbands is predicted from the other sub- band. It is observed that the adaptive subband decomposition performs better than a regulcir subband decomposition with a fixed filter bank in terms of compression. For the binary textual images, a compression algorithm using binary subband decomposition followed by a textual image compression (TIC) method that exploits the redundancy in repeating characters is developed. The binary subband decomposition yields binary sub-images, and the TIC method is applied to the low band sub-image. Obtaining binary sub-images improves compression results as well as pattern matching time of the TIC method. Simulation results for both adaptive subband decomposition and multiresolution TIC methods indicate improvements over the methods described in the literature.Gerek, Ömer NezihPh.D