Design and analysis of entropy-constrained reflected residual vector quantization

Residual vector quantization (RVQ) is a vector quantization (VQ) paradigm which imposes structural constraints on the encoder in order to reduce the encoding search burden and memory storage requirements of an unconstrained VQ. Jointly optimized RVQ (JORVQ) is an effective design algorithm for minimizing the overall quantization error. Reflected residual vector quantization (RRVQ) is an alternative design algorithm for the RVQ structure with a smaller computation burden. RRVQ works by imposing an additional symmetry constraint on the RVQ codebook design. Savings in computation were accompanied by an increase in distortion. However, an RRVQ codebook, being structured in nature, is expected to provide lower output entropy. Therefore, we generalize RRVQ to include noiseless entropy coding. The method is referred to as entropy-constrained RRVQ (EC-RRVQ). Simulation results show that EC-RRVQ outperforms RRVQ by 4 dB for memoryless Gaussian and Laplacian sources. In addition, for the same synthetic sources, EC-RRVQ provided an improvement over other entropy-constrained designs, such as entropy-constrained JORVQ (EC-JORVQ). The design performed equally well on image data. In comparison with EC-JORVQ, EC-RRVQ is simpler and outperforms the EC-JORVQ

Design and analysis of entropy-constrained reflected residual vector quantization

Residual vector quantization (RVQ) is a vector quantization (VQ) paradigm which imposes structural constraints on the encoder in order to reduce the encoding search burden and memory storage requirements of an unconstrained VQ. Jointly optimized RVQ (JORVQ) is an effective design algorithm for minimizing the overall quantization error. Reflected residual vector quantization (RRVQ) is an alternative design algorithm for the RVQ structure with a smaller computation burden. RRVQ works by imposing an additional symmetry constraint on the RVQ codebook design. Savings in computation were accompanied by an increase in distortion. However, an RRVQ codebook, being structured in nature, is expected to provide lower output entropy. Therefore, we generalize RRVQ to include noiseless entropy coding. The method is referred to as entropy-constrained RRVQ (EC-RRVQ). Simulation results show that EC-RRVQ outperforms RRVQ by 4 dB for memoryless Gaussian and Laplacian sources. In addition, for the same synthetic sources, EC-RRVQ provided an improvement over other entropy-constrained designs, such as entropy-constrained JORVQ (EC-JORVQ). The design performed equally well on image data. In comparison with EC-JORVQ, EC-RRVQ is simpler and outperforms the EC-JORVQ

Image coding using entropy-constrained reflected residual vector quantization

Residual vector quantization (RVQ) is a structurally constrained vector quantization (VQ) paradigm. RVQ employs multipath search and has higher encoding cost as compared to sequential single-path search. Reflected residual vector quantization (Ref-RVQ), a design with additional symmetry on the codebook, was developed later to a jointly optimized RVQ structure with single-path search. The constrained Ref-RVQ codebook exhibits an increase in distortion. However, it was conjectured that the Ref-RVQ codebook has a lower output entropy than that of the multipath RVQ codebook. Therefore, the Ref-RVQ design was generalized to include noiseless entropy coding. We apply it to image coding. The method is referred to as entropy-constrained Ref-RVQ (EC-Ref-RVQ). Since the RVQ scheme is able to implement very large dimensional vector quantization designs like 16/spl times/16 and 32/spl times/32 VQs, it is found highly successful in extracting linear and non-linear correlation among image pixels. We intend to implement these large dimensional vectors with the EC-Ref-RVQ scheme to realize a computationally less demanding image-RVQ design. Simulation results demonstrate that EC-Ref-RVQ, while maintaining single path search, provides 1 dB improvement in PSNR for image data over the multipath EC-RVQ

Higher order conditional entropy-constrained trellis-coded RVQ withapplication to pyramid image coding

This paper introduces an extension of conditional entropy-constrained residual vector quantization (CEC-RVQ) to include quantization cell shape gain. The method is referred to as conditional entropy-constrained trellis-coded RVQ (CEC-TCRVQ). The new design is based on coding image vectors by taking into account their 2D correlation and employing a higher order entropy model with a trellis structure. We employed CEC-TCRVQ to code image subbands at low bit rate. The CEC-TCRVQ coded images do well in term of preserving low-magnitude textures present in some image

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

Multiresolution vector quantization

Multiresolution source codes are data compression algorithms yielding embedded source descriptions. The decoder of a multiresolution code can build a source reproduction by decoding the embedded bit stream in part or in whole. All decoding procedures start at the beginning of the binary source description and decode some fraction of that string. Decoding a small portion of the binary string gives a low-resolution reproduction; decoding more yields a higher resolution reproduction; and so on. Multiresolution vector quantizers are block multiresolution source codes. This paper introduces algorithms for designing fixed- and variable-rate multiresolution vector quantizers. Experiments on synthetic data demonstrate performance close to the theoretical performance limit. Experiments on natural images demonstrate performance improvements of up to 8 dB over tree-structured vector quantizers. Some of the lessons learned through multiresolution vector quantizer design lend insight into the design of more sophisticated multiresolution codes

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

Network vector quantization

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples