Christopher F. Barnes

Advances in residual vector quantization: a review

Advances in residual vector quantization (RVQ) are surveyed. Definitions of joint encoder optimality and joint decoder optimality are discussed. Design techniques for RVQs with large numbers of stages and generally different encoder and decoder codebooks are elaborated and extended. Fixed-rate RVQs, and variable-rate RVQs that employ entropy coding are examined. Predictive and finite state RVQs designed and integrated into neural-network based source coding structures are revisited. Successive approximation RVQs that achieve embedded and refinable coding are reviewed. A new type of successive approximation RVQ that varies the instantaneous block rate by using different numbers of stages on different blocks is introduced and applied to image waveforms, and a scalar version of the new residual quantizer is applied to image subbands in an embedded wavelet transform coding system.

Vector quantizers with direct sum codebooks

The use of direct sum codebooks to minimize the memory requirements of vector quantizers is investigated. Assuming arbitrary fixed partitions, necessary conditions for minimum distortion codebooks are derived, first for scalar codebooks, assuming mean-squared error distortion, and then for vector codebooks and a broader class of distortion measures. An iterative procedure is described for designing locally optimal direct sum codebooks. Both optimal and computationally efficient suboptimal encoding schemes are considered. It is shown that although an optimal encoding can be implemented by a sequential encoder, the complexity of implementing optimal stagewise partitions generally exceeds the complexity of an exhaustive search of the direct sum codebook. It is also shown that sequential nearest-neighbor encoders can be extremely inefficient. The M-search method is explored as one method of improving the effectiveness of suboptimal sequential encoders. Representative results for simulated direct sum quantizers are presented. >

Residual vector quantizers with jointly optimized code books

Publisher Summary This chapter discusses the basic principles of minimum distortion quantization; both scalar and vector quantizers are considered. It also discusses the residual quantizer (RQ) structure and an alternative RQ representation used in subsequent analysis called the “equivalent single-stage quantizer” and the methods to optimize scalar RQs. The chapter also presents a derivation of necessary conditions for minimum distortion. In the chapter, the problem of encoding complexity is also considered, and the difficulties associated with tree-structured encoders for RQ are described and illustrated. A modified RQ alphabet based on stagewise reflection symmetry and termed reflected RQ (rRQ) is introduced. Further, comparison is drawn between the distortion and complexity of the exhaustive search vector quantizers, the unoptimized RQ, optimized RQ, and rRQ on a variety of synthetic and natural sources.

Successive approximation quantization with generalized decoding for wavelet transform image coding

A novel combination of a successive approximation scalar quantizer encoder structure and a direct sum decoder structure is introduced. The encoder structure is a multiple level free structure that corresponds to a conventional uniform scalar quantizer. The decoder structure is a multiple stage direct sum structure. The uniform quantizer encoder structure is matched to the dynamic range of the source output. The decoder direct sum structure is jointly optimized for the source probability density function and the fixed partition of the uniform quantizer encoder. The bit stream generated by the encoder can be decoded either by the standard uniform quantizer decoder, or by the generalized nonuniform direct sum decoder described. Successive approximation multiple stage scalar quantizers with both standard and generalized decoders are tested on image wavelet transform coefficients. The generalized codes give approximately 0/spl sim/7 dB improvements over standard codes for one to eight bit representations of real-valued wavelet coefficients.<<ETX>>

A new multiple path search technique for residual vector quantizers

Multiple path searching can provide varying degrees of joint search optimization of residual vector quantizer encoder stages. A short coming of the conventional multiple path M-search algorithm, however, is that joint search optimization of encoder stages is limited to consecutive stages. A new iterated multipath (IM)-search algorithm is introduced that is not subject to any particular ordering of the residual quantizer stages. The IM-search algorithm may be combined with the sequential M-search algorithm to provide additional enhancement of residual vector quantization encoder performance. Furthermore, additional details of design methods for residual quantizers with separate, and, in general, different encoder and decoder cookbooks are given. Separate encoder and decoder cookbooks facilitate the use and design of various suboptimal, but computationally efficient encoder structures, while maintaining the use of decoder stage codebooks which satisfy necessary conditions for the joint optimality of direct sum codebooks.<<ETX>>

Detection of mine and minelike objects in forward-looking sonar data with direct sum successive approximation templates

Nearest neighbor classifiers with direct sum successive approximation (DSSA) templates are shown to be effective for detecting and discriminating mines and mine-like objects in forward looking sonar data. DSSA results are demonstrated on data obtained form field measurements with actual mines and calibration targets. The DSSA templates are used in a nearest neighbor classifier that can be characterized as a new type of radial basis function neural network. This neural network is not designed with a preset complexity level as quantified by an a priori determined number of degrees-of-freedom. Rather, the system is constructed incrementally and adds additional degrees-of-freedom as required by the nature of the training data. The neural net system possesses stage structure that result in inherent computational and memory efficiency in searching and storing the DSSA-based radial basis functions.

Adaptive successive approximation quantization of image waveforms with efficient codebook updates

A design method for adaptive successive approximation residual vector quantizers with suboptimal but computationally efficient sequential search encoders is given. Image-specific codebook adaptation and the sequential search encoder structural constraint are shown to be more easily accommodated with the use of separate, and in general, different encoder and decoder code books. The design method generates encoder codebooks that provide computationally efficient successive approximation tree structures, and generates decoder codebooks that satisfy conditions necessary for joint optimality. Design monotonicity is maintained even with the use of small training sets sizes, as required by image-specific codebook adaptation. The memory advantage of the direct sum structure permits image adapted codebooks to be efficiently stored or transmitted as overhead information.<<ETX>>

Fast-search nearest neighbor classification based on structured templates

A mine detection algorithm based on the us of structured templates applied to acoustic backscatter data is proposed. The structured templates correspond to the codevectors of a type of cluster-based compression algorithm called residual vector quantization (RVQ). The RVQ clusters have a hierarchical structure that permits efficient searches for nearest neighbor templates, and efficient dictionary storage for memory cost reduction. The structured templates are generated by a multistage synthesis process that produces a sequence of finite precision representations of training data. This successive approximation process is combined with a sequential classification process to form a new type of classifier called a direct sum successive approximation classifier.

Embedded wavelet zerotree coding with direct sum quantization structures

One of the more effective data compression systems that has been recently proposed is the relatively simple embedded wavelet image coder developed by J.M. Shapiro (1994). Two key components of Shapiros system are the use of zerotrees to keep track of insignificant subband coefficients and progressive transmission of successive bit planes of significant coefficients. Shapiros quantization mechanism is the use of scaled successive approximation uniform scalar quantizers. This paper investigates ways of improving the performance of embedded wavelet coders with the use of optimized successive approximation direct sum quantization structures.