Abstract: Adaptive k-means clustering algorithms have been used in several artificial neural network architectures, such as radial basis function networks or feature-map classifiers, for a competitive partitioning of the input domain. This paper presents an enhancement of the traditional k-means algorithm. It approximates an optimal clustering solution with an efficient adaptive learning rate, which renders it usable even in situations where the statistics of the problem task varies slowly with time. This modification Is based on the optimality criterion for the k-means partition stating that: all the regions in an optimal k-means partition have the same variations if the number of regions in the partition is large and the underlying distribution for generating input patterns is smooth. The goal of equalizing these variations is introduced in the competitive function that assigns each new pattern vector to the "appropriate" region. To evaluate the optimal k-means algorithm, the authors first compare it to other k-means variants on several simple tutorial examples, then the authors evaluate it on a practical application: vector quantization of image data. >

Abstract: A weighted wavelet hierarchical vector quantization (WWHVQ) procedure is initiated by obtaining an N×N pixel image where 8 bits per pixel (steps 10 and 12). A look-up operation is performed to obtain data representing a discrete wavelet transform (DWT) followed by a quantization of the data (step 14). Upon completion of the look-up, a data compression will have been performed. Further stages and look-up will result in further compression of the data, i.e., 4:1, 8:1, 16:1, 32:1, 64:1, . . . etc. Accordingly, a determination is made whether the compression is complete (step 16). If the compression is incomplete, further look-up is performed. If the compression is complete, however, the compressed data is transmitted (step 18). It is determined at a gateway whether further compression is required (step 19). If so, transcoding is performed (step 20). The receiver receives the compressed data (step 22). Subsequently, a second look-up operation is performed to obtain data representing an inverse discrete wavelet transform of the decompressed data (step 24). After one iteration, the data is decompressed by a factor of two. Further iterations allows for further decompression of the data. Accordingly, a determination is made whether decompression is complete (step 26). If the decompression is in incomplete, further look-ups are performed. If, however, the decompression is complete, the WWHVQ procedure is ended (step 28).

Abstract: Improved method and apparatus for vector quantization (VQ) to build a codebook for the compression of data. The codebook or "tree" is initialized by establishing N initial nodes and creating the remainder of the codebook as a binary codebook. Children entries are split upon determination of various attributes, such as maximum distortion, population, etc. Vectors obtained from the data are associated with the children nodes, and then representative children entries are recalculated. This splitting/reassociation continues iteratively until a difference in error associated with the previous children and current children becomes less than a threshold. This splitting and reassociating process continues until the maximum number of terminal nodes is created in the tree, a total error or distortion threshold has been reached or some other criterion. The data may then be transmitted as a compressed bitstream comprising a codebook and indices referencing the codebook.

Abstract: A new technique to recover the information loss in a block-based image coding system is developed in this paper. The proposed scheme is based on fuzzy logic reasoning and can be divided into three main steps: (1) hierarchical compass interpolation/extrapolation (HCIE) in the spatial domain for initial recovery of lost blocks that mainly contain low-frequency information such as smooth background (2) coarse spectra interpretation by fuzzy logic reasoning for recovery of lost blocks that contain high-frequency information such as complex textures and fine features (3) sliding window iteration (SWI), which is performed in both spatial and spectral domains to efficiently integrate the results obtained in steps (1) and (2) such that the optimal result can be achieved in terms of surface continuity on block boundaries and a set of fuzzy inference rules. The proposed method, which is suitable for recovering both isolated and contiguous block losses, provides a new approach for error concealment of block-based image coding systems such as the JPEG coding standard and vector quantization-based coding algorithms. The principle of the proposed scheme can also be applied to block-based video compression schemes such as the H.261, MPEG, and HDTV standards. Simulation results are presented to illustrate the effectiveness of the proposed method. >

Abstract: This paper extends Bennett's (1948) integral from scalar to vector quantizers, giving a simple formula that expresses the rth-power distortion of a many-point vector quantizer in terms of the number of points, point density function, inertial profile, and the distribution of the source. The inertial profile specifies the normalized moment of inertia of quantization cells as a function of location. The extension is formulated in terms of a sequence of quantizers whose point density and inertial profile approach known functions as the number of points increase. Precise conditions are given for the convergence of distortion (suitably normalized) to Bennett's integral. Previous extensions did not include the inertial profile and, consequently, provided only bounds or applied only to quantizers with congruent cells, such as lattice and optimal quantizers. The new version of Bennett's integral provides a framework for the analysis of suboptimal structured vector quantizers. It is shown how the loss in performance of such quantizers, relative to optimal unstructured ones, can be decomposed into point density and cell shape losses. As examples, these losses are computed for product quantizers and used to gain further understanding of the performance of scalar quantizers applied to stationary, memoryless sources and of transform codes applied to Gaussian sources with memory. It is shown that the short-coming of such quantizers is that they must compromise between point density and cell shapes. >

Abstract: The combination of singular value decomposition (SVD) and vector quantization (VQ) is proposed as a compression technique to achieve low bit rate and high quality image coding. Given a codebook consisting of singular vectors, two algorithms, which find the best-fit candidates without involving the complicated SVD computation, are described. Simulation results show that the proposed methods are better than the discrete cosine transform (DCT) in terms of energy compaction, data rate, image quality, and decoding complexity. >

Abstract: One of the most serious problems for vector quantization, especially for high dimensional vectors, is the high computational complexity of searching for the closest codeword in the codebook design and encoding phases. Although quantizing high dimensional vectors rather than low dimensional vectors results in better performance, the computation time needed for vector quantization grows exponentially with the vector dimension. This makes high dimensional vectors unsuitable for vector quantization. To overcome this problem, a fast search algorithm, under the assumption that the distortion is measured by the squared Euclidean distance, is proposed. Using the mean pyramids of codewords, the algorithm ran reject many codewords that are impossible matches and hence save a great deal of computation time. The algorithm is efficient for high dimensional codeword searches. Experimental results confirm the effectiveness of the proposed method. >

Abstract: A new audio-coding method is proposed. This method is called transform-domain weighted interleave vector quantization (TwinVQ) and achieves high-quality reproduction at less than 64 kbit/s. The method is a transform coding using modified discrete cosine transform (MDCT). There are three novel techniques in this method: flattening of the MDCT coefficients by the spectrum of linear predictive coding (LPC) coefficients; interframe backward prediction for flattening the MDCT coefficients; and weighted interleave vector quantization. Subjective evaluation tests showed that the quality of the reproduction of TwinVQ exceeded that of an MPEG Layer II coder at the same bitrate.

Abstract: An apparatus and method of quantizing a sequence of input data vectors using delayed decision switched prediction and vector quantization. The method has the following steps of operation: (a) predicting a next vector element from said sequence of input data vectors to generate a set of prediction vectors; (b) subtracting the set of prediction vectors from the next vector element to generate a set of prediction error vectors; (c) multi-stage vector quantizing the set of prediction error vectors to generate a set of quantized prediction error vectors with each of the stages having at least one of the tables and local decision means to generate a final quantization error vector according to a predetermined distance measure; (d) selecting one predictor out of the set of predictors from the switched prediction step and selecting, for each of the stages, at least one entry from the set of tables of the vector quantization step according to the predetermined distance measure, generating a quantized data vector.

Abstract: Power normalization parts calculate the average powers of input signals of a plurality of channels for each frame and divide the signals by the calculated average powers to generate normalized signals and, at the same time, generate weights corresponding to the normalization gains. The normalized signals of the plurality of channels are combined in a combining part into predetermined sequences and outputted therefrom as one or more interleaved signal vectors. The combining part combines the weights from the power normalization part into the same sequences of the normalized signal and outputs one or more interleaved weight vectors. In a vector quantization part the signal vectors are vector quantized by the interleaved weight vectors corresponding thereto, respectively, and quantization indexes and normalization indexes are outputted as results of coding.

Abstract: A video image encoder estimates a quantization noise curve which will result from quantizing a coefficient data block and uses the estimated quantization noise curve and a specified minimum noise value to select the quantization step size actually used to quantize the coefficient data block. The quantization step size is also selected as a function of transmission buffer occupancy so as to limit the amount of encoded data to a predetermined rate.

Abstract: The problem of scalar and vector quantization in conjunction with a noisy binary symmetric channel is considered. The issue is the assignment of the shortest possible distinct binary sequences to quantization levels or vectors so as to minimize the mean-squared error caused by channel errors. By formulating the assignment as a matrix (or vector in the scalar case) and showing that the mean-squared error due to channel errors is determined by the projections of its columns onto the eigenspaces of the multidimensional channel transition matrix, a class of source/quantizer pairs is identified for which the optimal index assignment has a simple and natural form. Among other things, this provides a simpler and more accessible proof of the result of Crimmins et al. (1969) that the natural binary code is an optimal index assignment for the uniform scalar quantizer and uniform source. It also provides a potentially useful approach to further developments in source-channel coding.

Abstract: We introduce a two-stage universal transform code for image compression. The code combines Karhunen-Loeve transform coding with weighted universal bit allocation (WUBA) in a two-stage algorithm analogous to the algorithm for weighted universal vector quantization (WUVQ). The encoder uses a collection of transform/bit allocation pairs rather than a single transform/bit allocation pair (as in JPEG) or a single transform with a variety of bit allocations (as in WUBA). We describe both an encoding algorithm for achieving optimal compression using a collection of transform/bit allocation pairs and a technique for designing locally optimal collections of transform/bit allocation pairs. We demonstrate the performance using the mean squared error distortion measure. On a sequence of combined text and gray scale images, the algorithm achieves up to a 2 dB improvement over a JPEG style coder using the discrete cosine transform (DCT) and an optimal collection of bit allocations, up to a 3 dB improvement over a JPEG style coder using the DCT and a single (optimal) bit allocation, up to 6 dB over an entropy constrained WUVQ with first- and second-stage vector dimensions equal to 16 and 4 respectively, and up to a 10 dB improvement over an entropy constrained vector quantizer (ECVQ) with a vector dimension of 4.

Abstract: A new algorithm is developed for the vector quantization of motion vectors. This algorithm, called motion vector quantization (MVQ), simultaneously estimates and vector quantizes the motion vectors by reinterpreting the block matching algorithm as a type of vector quantization. An iterative design algorithm, based on this concept, is developed. In addition to reducing rate for fixed length encoding, the algorithm also reduces the computation considerably. We include coding simulation results on the Flower Garden sequence

Abstract: Image and video compression has become an increasingly important and active area. Many techniques have been developed in this area. Any compression technique can be modeled as a three-stage process. The first stage can be generally called a signal processing stage where an image or video signal is converted into a different domain. Usually, there is no or little loss of information in this stage. The second stage is quantization where loss of information occurs. The third stage is lossless coding that generates the compressed bit stream. The purpose of the signal processing stage is to convert an image or video signal into such a form that quantization can achieve better performance than without the signal processing stage. Because the quantization stage is the place where most of compression is achieved and loss of information occurs, it is naturally the central stage of any compression technique. Since scalar quantization or vector quantization may be used in the second stage, the operation in the first stage should be scalar-based or vector-based respectively in order to match the second stage so that the compression performance can be optimized. In this paper, we summarize the most recent research results on vector-based signal processing and quantization techniques that have shown high compression performance. >

Abstract: In this paper, we propose a new technique for the storage and retrieval of compressed images. Here, the images are compressed using vector quantization and the codebook is used to generate a feature vector. This feature vector is used as an index to access the images in the database. This technique combines image compression with image indexing. In addition, it has lower storage and computation requirements compared with other techniques reported in the literature. >

Abstract: Necessary conditions for the optimality of variable-rate residual vector quantizers are derived, and an iterative descent algorithm based on a Lagrangian formulation is introduced for designing residual vector quantizers having minimum average distortion subject to an entropy constraint. Simulation results for entropy-constrained residual vector quantizers are presented for memoryless Gaussian, Laplacian, and uniform sources. A Gauss-Markov source is also considered. The rate-distortion performance is shown to be competitive with that of entropy-constrained vector quantization and entropy-constrained trellis-coded quantization.

Abstract: An image coder based on the singular value decomposition and vector quantization is presented. The singular values and singular vectors of the image subblocks are computed at the encoder and quantized using a novel variable bit-rate coding scheme. The performance of the coder is assessed by computer simulations.

Abstract: An improved wavelet compression algorithm for ECG signals has been developed with the use of vector quantization on wavelet coefficients. Vector quantization on scales of long duration and low dynamic range retains feature integrity of the ECG with a very low bit-per-sample rate. Preliminary results indicate that the proposed method excels over standard techniques for high fidelity compression. >

Abstract: An efficient coding scheme for linear predictive coding (LPC) residuals is proposed based on harmonic and noise representation. New features of the scheme include classified vector quantization of the spectral envelope of LPC residuals with a weighted distortion measure. The improvement in performance obtained by classifying codebooks based on a voiced/unvoiced (V/UV) decision is shown. Sequences of the short-term RMS power of the time domain waveforms are also vector quantized and transmitted for unvoiced signals. A fast synthesis algorithm for voiced signals using an FFT is also presented, which reduces the high complexity of the direct sinusoidal synthesis method with interpolated magnitudes and phases. Informal listening tests indicate that, in combination with a known LSP quantization technique, this residual coding scheme provides good communication quality at a total bit rate of less than 2.0 kbps.

Abstract: An N-stage vector quantizer in which increasingly smaller portions of a vector are compared to a threshold until the quantization error is less than the threshold. The threshold may be adaptive to insure a constant bit rate. The first stage performs VQ and inverse VQ on an input vector. The difference between the inverse VQ and the input vector is determined to create a first stage residual error. If the first stage residual error is less than a threshold, no further stages of the multistage vector quantizer are used and the input vector or first stage residual is passed on to the output stage. However, if the first stage residual error is not less than the threshold, the residual error is passed to stage two of the multistage vector quantizer where VQ and inverse VQ are performed on the first stage residual error. The process is continued until the residual is less than the threshold. If the Nth stage is reached without the residual being less than the threshold, the process is repeated on a smaller portion of the original input vector. For example, if the original input vector were a 16×16 vector, the smaller section could be a 16×8 vector.

Abstract: Proposes an efficient vector quantization (VQ) technique called sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit intercomponent correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, the authors appeal to asymptotic quantization theory, where the codebook size is assumed to be large. Closed-form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. The authors also demonstrate the use of asymptotic theory in designing SSQ for a practical application (color image quantization), where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE. >

Abstract: Vector quantization (VQ) and block truncation coding (BTC) are successful image compression techniques. However, a reproduced image using VQ or BTC suffers from edge degradation. A new technique that combines the advantages of both VQ and BTC to combat this degradation is presented and is referred to as VQ-BTC. In VQ-BTC, a low-detail block is encoded using VQ. For a high-detail block, a modification of BTC is used to determine the locations of the relatively lighter and relatively darker pixels inside the block and VQ is then used to encode each. VQ-BTC provides improved edge reproduction and much lower bit rates than those obtained by BTC. >

Abstract: Colour image quantization is the process of representing an image with a small number of well selected colours. Most previous colour quantization techniques use a recursive pre-clustering approach. These algorithms subdivide the colour space into a set of simple geometric regions. Thus, the colour map is chosen on the basis of this approximation. We propose a new quantization method called local K-means (LKM).1t is an iterative post-clustering technique that approximates an optimal palette using multiple subsets of image points. The paper also presents ways to speedup the search of the closest colour for a dynamically changing palette. The local K-means procedure is compared with popular pre-clustering algorithms. The LKM method is able to generate a high quality palette significantly fast er than other quantization techniques.

Abstract: A method and apparatus for recording digital video signals in which digital video signals in the form of DCT coefficients, obtained by e.g., discrete cosine transform, are quantized and compressed so as to be recorded on a recording medium. A first quantization step decision unit determines a quantization step in terms of a video segment made up of plural macro-blocks as a unit so that the quantity of quantized data is less than a pre-set data quantity. A second quantization step decision unit determines a quantization step in terms of the macro-blocks as a unit so that the quantity of quantized data is less than the pre-set data quantity. A quantization unit quantizes the digital video signals with the quantization steps determined by the first quantization step decision unit and the second quantization step decision unit. This enables efficient encoding and improved picture quality.