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${\cal {D}}$-invariant, order-increasing group lifting structures, it is shown that the associated lifting cascade group${\cal {C}}$is isomorphic to the free product of the upper and lower triangular lifting matrix groups. Under the same hypotheses, the associated scaled lifting group${\cal {S}}$is the semidirect product of${\cal {C}}$by the diagonal gain scaling matrix group${\cal {D}}$. 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,${\cal {W}}$, that is in fact equal to its own scaled lifting group,${\cal {W}}={\cal {S}}_{{\cal {W}}}$, the results of this paper characterize the group-theoretic structure of${\cal {W}}$up to isomorphism. Although the half-sample symmetric class${\Fraktur {H}}$does not form a group, it can be partitioned into cosets of its lifting cascade group,${\cal {C}}_{\Fraktur {H}}$, or, alternatively, into cosets of its scaled lifting group,${\cal {S}}_{\Fraktur {H}}$. Homomorphic comparisons reveal that scaled lifting groups covered by the results in this paper have a structure analogous to a “noncommutative vector space.”

The joint photographic experts group (JPEG) committee (ISO/IEC JTC1/SC29/WG1) is currently pursuing the standardization of a three-dimensional extension of the JPEG-2000 standard (Parts 1 and 2) to support the encoding of volumetric data sets. This extension, Part 10 - extensions for three-dimensional data (JP3D), will support functionalities like resolution scalability, quality scalability and region-of-interest coding, while exploiting the entropy in the additional third dimension to improve the rate-distortion performance. In this paper, we give an overview of the markets and application areas targeted by JP3D, the imposed requirements and the algorithm under study

A new digital image compression standard has been adopted by the US Federal Bureau of Investigation for use on digitized gray-scale fingerprint images. The algorithm is based on adaptive uniform scalar quantization of a discrete wavelet transform image decomposition and is referred to as the wavelet/scalar quantization standard. The standard produces archival quality images at compression ratios of around 20:1 and will allow the FBI to replace their current database of paper fingerprint cards with digital imagery.>

A new procedure for efficient compression of digital information for storage and transmission purposes involves a discrete wavelet transform subband decomposition of the data set, followed by vector quantization of the wavelet transform coefficients using application-specific vector quantizers. The vector quantizer design optimizes the assignment of both memory resources and vector dimensions to the transform subbands by minimizing an exponential rate-distortion functional subject to constraints on both overall bit-rate and encoder complexity. The method is applicable to the compression of other multidimensional data sets possessing some degree of smoothness. The authors discuss the use of this technique for compressing the output of supercomputer simulations of global climate models. The data presented here comes from Semtner-Chervin global ocean models run at the National Center for Atmospheric Research.>

A new method is introduced for reconstructing a signal from an incomplete sampling of its discrete wavelet transform (DWT). The algorithm yields a minimum-norm estimate satisfying a priori upper and lower bounds on the signal. The method is based on a finite-dimensional representation theory for minimum-norm estimates of bounded signals developed by Cole (1990). Cole's work provides a representation for minimum-norm estimates of a class of generalized transforms in terms of general correlation data (not just DFTs of autocorrelation lags, as in spectral estimation). One virtue of this great generality is that it includes the inverse DWT.>