Vector quantization

During the past ten years Vector Quantization (VQ) has developed from a theoretical possibility promised by Shannon's source coding theorems into a powerful and competitive technique for speech and image coding and compression at medium to low bit rates. In this survey, the basic ideas behind the design of vector quantizers are sketched and some comments made on the state-of-the-art and current research efforts

A vector quantization approach to universal noiseless coding and quantization

A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n -1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n-1) when the universe of sources is countable, and as O(n-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions

Weighted universal image compression

We describe a general coding strategy leading to a family of universal image compression systems designed to give good performance in applications where the statistics of the source to be compressed are not available at design time or vary over time or space. The basic approach considered uses a two-stage structure in which the single source code of traditional image compression systems is replaced with a family of codes designed to cover a large class of possible sources. To illustrate this approach, we consider the optimal design and use of two-stage codes containing collections of vector quantizers (weighted universal vector quantization), bit allocations for JPEG-style coding (weighted universal bit allocation), and transform codes (weighted universal transform coding). Further, we demonstrate the benefits to be gained from the inclusion of perceptual distortion measures and optimal parsing. The strategy yields two-stage codes that significantly outperform their single-stage predecessors. On a sequence of medical images, weighted universal vector quantization outperforms entropy coded vector quantization by over 9 dB. On the same data sequence, weighted universal bit allocation outperforms a JPEG-style code by over 2.5 dB. On a collection of mixed test and image data, weighted universal transform coding outperforms a single, data-optimized transform code (which gives performance almost identical to that of JPEG) by over 6 dB

An iterative joint codebook and classifier improvement algorithm for finite-state vector quantization

A finite-state vector quantizer (FSVQ) is a multicodebook system in, which the current state (or codebook) is chosen as a function of the previously quantized vectors. The authors introduce a novel iterative algorithm for joint codebook and next state function design of full search finite-state vector quantizers. They consider the fixed-rate case, for which no optimal design strategy is known. A locally optimal set of codebooks is designed for the training data and then predecessors to the training vectors associated with each codebook are appropriately labelled and used in designing the classifier. The algorithm iterates between next state function and state codebook design until it arrives at a suitable solution. The proposed design consistently yields better performance than the traditional FSVQ design method (under identical state space and codebook constraints)

A mean-removed variation of weighted universal vector quantization for image coding

Weighted universal vector quantization uses traditional codeword design techniques to design locally optimal multi-codebook systems. Application of this technique to a sequence of medical images produces a 10.3 dB improvement over standard full search vector quantization followed by entropy coding at the cost of increased complexity. In this proposed variation each codebook in the system is given a mean or 'prediction' value which is subtracted from all supervectors that map to the given codebook. The chosen codebook's codewords are then used to encode the resulting residuals. Application of the mean-removed system to the medical data set achieves up to 0.5 dB improvement at no rate expense

A Progressive Universal Noiseless Coder

The authors combine pruned tree-structured vector quantization (pruned TSVQ) with Itoh's (1987) universal noiseless coder. By combining pruned TSVQ with universal noiseless coding, they benefit from the “successive approximation” capabilities of TSVQ, thereby allowing progressive transmission of images, while retaining the ability to noiselessly encode images of unknown statistics in a provably asymptotically optimal fashion. Noiseless compression results are comparable to Ziv-Lempel and arithmetic coding for both images and finely quantized Gaussian sources

Comparison of large and small tropical cyclones, A

July, 1982.Includes bibliographical references.Sponsored by NOAA NA81RAD00005.Sponsored by NOAA NA8IRAH00001.Sponsored by NSF ATM-7923591

Study of tornado proximity data and an observationally derived model of tornado genesis, A

November 1973.Includes bibliographical references.Sponsored by NOAA 04-3-158-51

The IGF1 small dog haplotype is derived from Middle Eastern gray wolves

Abstract Background A selective sweep containing the insulin-like growth factor 1 (IGF1) gene is associated with size variation in domestic dogs. Intron 2 of IGF1 contains a SINE element and single nucleotide polymorphism (SNP) found in all small dog breeds that is almost entirely absent from large breeds. In this study, we surveyed a large sample of grey wolf populations to better understand the ancestral pattern of variation at IGF1 with a particular focus on the distribution of the small dog haplotype and its relationship to the origin of the dog. Results We present DNA sequence data that confirms the absence of the derived small SNP allele in the intron 2 region of IGF1 in a large sample of grey wolves and further establishes the absence of a small dog associated SINE element in all wild canids and most large dog breeds. Grey wolf haplotypes from the Middle East have higher nucleotide diversity suggesting an origin there. Additionally, PCA and phylogenetic analyses suggests a closer kinship of the small domestic dog IGF1 haplotype with those from Middle Eastern grey wolves. Conclusions The absence of both the SINE element and SNP allele in grey wolves suggests that the mutation for small body size post-dates the domestication of dogs. However, because all small dogs possess these diagnostic mutations, the mutations likely arose early in the history of domestic dogs. Our results show that the small dog haplotype is closely related to those in Middle Eastern wolves and is consistent with an ancient origin of the small dog haplotype there. Thus, in concordance with past archeological studies, our molecular analysis is consistent with the early evolution of small size in dogs from the Middle East. See associated opinion by Driscoll and Macdonald: http://jbiol.com/content/9/2/1