Abstract: Self-organizing maps have a connection with traditional vector quantization. A characteristic which makes them resemble certain biological brain maps, however, is the spatial order of their responses which is formed in the learning process. Two innovations are discussed: dynamic weighting of the input signals at each input of each cell, which improves the ordering when very different input signals are used, and definition of neighborhoods in the learning algorithm by the minimum spanning tree, which provides a far better and faster approximation of prominently structured density functions. It is cautioned that if the maps are used for pattern recognition and decision processes, it is necessary to fine-tune the reference vectors such that they directly define the decision borders. >

Abstract: Image encoding apparatus and methods include recursively decomposing the luminance values of sequential frames into spatio-temporal spectral components, by quadrature mirror filter (QMF) processing of the luminance values The filtered signals are subsampled, and each decomposed level of the spectral components is coded by vector quantization

Abstract: A technique is presented for determining the probability density function (PDF) and variance of the quantization error of a sinusoidal signal applied to a uniform quantizer, namely, an ideal analog-digital converter. The results are the basis for determining the validity of the uniform quantization noise model for this class of signals. When dither is used it tends to decorrelate quantization error and the input signal. The effect of added uniform dither on the PDF of the quantizer input is investigated, as well as the PDF of the quantization error corresponding to the dithered sinusoid. The results prove the validity of the uniform quantization model in this case. >

Abstract: A harmonic speech coding arrangement where vector quantization is used to improve speech quality Parameters are determined at the analyzer (120) of an illustrative coding arrangement to model the magnitude and phase spectra of the input speech A first codebook of vectors is searched for a vector that closely approximates the difference between the true and estimated magnitude spectra A second codebook of vectors is searched for a vector that closely approximates the difference between the true and the estimated phase spectra Indices and scaling factors for the vectors are communicated to the synthesizer (160) such that scaled vectors can be added into the magnitude and phase spectra for use at the synthesizer in generating speech as a sum of sinusoids

Abstract: A geometric formulation is presented for source coding and vector quantizer design. Motivated by the asymptotic equipartition principle, the authors consider two broad classes of source codes and vector quantizers: elliptical codes and quantizers based on the Gaussian density function, and pyramid codes and quantizers based on the Laplacian density function. Elliptical and weighted pyramid vector quantizers are developed by selecting codewords as points in a lattice that lie on (or near) a specified ellipse or pyramid. The combination of geometric structure and lattice basis allows simple encoding and decoding algorithms. >

Abstract: Recently, C.D. Bei and R.M. Gray (1985) used a partial distance search algorithm that reduces the computational complexity of the minimum distortion encoding for vector quantization. The effect of ordering the codevectors on the computational complexity of the algorithm is studied. It is shown that the computational complexity of this algorithm can be reduced further by ordering the codevectors according to the sizes of their corresponding clusters. >

Abstract: An adaptive image coding scheme, called classified transform vector quantization, is proposed. It efficiently exploits correlation in large image blocks by taking advantage of transform coding (TC) and vector quantization (VQ), while overcoming the suboptimalities of TC and avoiding the complexity obstacle of VQ. After local mean luminance values are removed in the spatial domain using two-stage interpolative VQ, the residual errors are encoded in the transform domain by means of perceptual block classification and adaptive subvector construction. This scheme avoids the use of scalar quantization of DC coefficients in the transform domain and yet substantially reduces the blocking effect that tends to arise at low bit rates. Good reconstructed images have been obtained at rates between 0.3 and 0.4 bits/pixel, depending on the nature of the test images. The technique also permits progressive image transmission and reproduces errorless images with compression of about 5.0 bits/pixel. Experimental results indicate that an efficient bit allocation in the coding process produces a substantial improvement in performance. >

Abstract: A progressive image transmission scheme in which vector quantization is applied to images represented by pyramids is proposed. A mean pyramid representation of an image is first built up by forming a sequence of reduced-size images by averaging over blocks of 2*2 pixels. A difference pyramid is then built up by taking the differences between successive levels in the mean pyramid. Progressive transmission is achieved by sending all the nodes in the difference pyramid starting from the top level and ending at the bottom level. The kth approximate image can be formed by adding the information of level k to the previously reproduced (k-1)st approximation. To gain efficiency, vector quantization is applied to the difference pyramid of the image on a level-by-level basis. If the errors due to quantization at level k are properly delivered and included in the next level, k+1, then it is demonstrated that the original image can be reconstructed. An entropy coder is used to encode the final residual error image losslessly, thus ensuring perfect reproduction of the original image. The experiments demonstrate that it is possible to achieve simultaneously lossless and progressive transmission with compression. At the intermediate level, the use of vector quantization results in a coding gain over that obtained using only a Huffman coder. Excellent reproduction is achieved at a bit rate of only 0.06 bits/pixel. >

Abstract: We present a method of vector quantisation which trades off accuracy for speed of encoding. We achieve this by hierarchically structuring a multistage encoder so that each stage encodes low dimensional input vectors. Such hierarchical encoders may easily be realised as a set of fast table look-up operations. We demonstrate how the Euclidean distortion in such a multistage encoder is approximately minimised by using Kohonen's topographic mapping learning algorithm from neural network theory. We also demonstrate the performance of the technique on various stochastic time series. We find that there is little loss in encoding accuracy, when compared with the exact nearest neighbour encoding using an equivalent single stage encoder.

Abstract: A vector quantization based image compression technique which exploits inter-block correlation and layered addressing structure to form variable block sizes. Without introducing any quality degradation, when compared to the traditional vector quantization algorithms, the invention described herein significantly increases the compression and reduces the bit rate. The concept of inter-block correlation is utilized to form variable size blocks, which are then coded using a hierarchical coding model. The method is based on starting off from a small basic block which is allowed to grow to a maximum of a preset block size as long as certain conditions are met. The basic idea of growing the block is based on the renormalization group theory in physics. The algorithm utilizes only one pixel code book for the basic block size and several address code books for the layer block sizes to encode an image. S/N ratio in excess of 30 dB at bit rates lower than 0.2 bpp are easily obtained.

Abstract: The authors present a very efficient minimum mean-squared error (MMSE) encoding method useful for vector quantization. Using this method results in a considerable reduction in the number of multiplications and additions. The increase in the number of comparisons is moderate, and therefore the overall saving in the number of operations is still considerable. Very little precomputation and extra storage is required. >

Abstract: The authors present an algorithm for the generation of codebooks from a set of training vectors using simulated annealing. Convergence of the algorithm to the globally optimal codebook in finite time is proved, and experimental results comparing simulated annealing with Lloyd algorithms for image quantization are presented. The experimental results indicate that the proposed algorithm obtains the best known codebook for the experimental situation described by R.M. Gray and E.D. Karnin (IEEE Trans. on Inf. Theory, vol.IT-28, no.2, p.256-61, Mar. 1982). It has also been demonstrated that this technique works well for the construction of codebooks from real image data. >

Abstract: A practical high-throughput architecture and its implementation for real-time coding of television-quality signals are presented. The architecture is directed toward the implementation of multistage vector quantization (VQ), as the authors' simulation results show that the latter is more suitable for real-time coding. However, the implementation is suitable for both single-stage and multistage VQ. The functional blocks of the VQ encoder system have been designed and implemented in VLSI technology. The VQ encoding scheme designed has an encoding delay of 25 clock cycles and is independent of the codebook size. >

Abstract: An easily implementable stochastic relaxation algorithm for vector quantisation design is given. It generalises the usual Lloyd iteration in codebook design by perturbing the computed entroids with independent multidimensional noise, whose variance diminishes as the algorithm progresses. A significant improvement is often achieved.

Abstract: Blocks of an image or voice input signal are decimated by a selected factor d, (e.g., d=2) and distributed through a plurality (d2) of ordered channels for vector quantization coding using a codebook in which vectors are ordered, such as by their average intensity. The first channel makes a full search of stored vectors in the codebook for a best match and outputs the index m.sup.(1) of the best match. The second channel makes a partial search for a best match over a localized region of the codebook around the index m.sup.(1) and outputs the index m.sup.(2) of the best match. The subsequent channels make partial searches over a smaller localized region of the codebook around an index that is a function of the indices m.sup.(1) and m.sup.(2). At the decoder, the indices m.sup.(1), m.sup.(2), m.sup.(3) and m.sup.(4) are used to look up vectors in a codebook identical to the coder codebook. These vectors are then assembled by a process that is the inverse of the decimation and distribution process at the encoder to output a decoded signal that is high quality replica of the input signal. The narrow search ranges in the channels following the first reduce the encoding search time and bit rate for each of the input blocks. That range may be readily changed for each channel, and therefore may be made adaptive.

Abstract: A semicontinuous hidden Markov model (HMM), which can be considered as a special form of continuous-mixture HMM with the continuous output probability density functions sharing in a mixture Gaussian density codebook, is proposed. The semicontinuous output probability density function is represented by a combination of the discrete output probabilities of the model and the continuous Gaussian density functions of a mixture Gaussian density codebook. The amount of training data required, as well as the computational complexity of the semicontinuous HMM, can be reduced in comparison to the continuous-mixture HMM. Parameters of the codebook and HMM can be mutually optimized to achieve an optimal model/codebook combination, which leads to a unified modeling approach to vector quantization and hidden Markov modeling of speech signals. Experimental results are included which show that the recognition accuracy of the semicontinuous HMM is measurably higher than those of both the discrete and the continuous HMM. >

Abstract: A system for voice coding based on vector quantization has an apparatus (108) in which a distri­bution area of parameters representative of a voice is divided into a plurality of domains so that one vector (code vector) may correspond to one domain, an apparatus (108) for representing individual code vectors by codes specific thereto, an apparatus (108) for converting an input voice into a vector and determining membership functions by numerically expressing the distance between the nearest code vector and each of the predetermined number of neighboring vectors, and an apparatus (111) for transmitting, as fuzzy vector quantization infor­mation, a code of the nearest code vector and the membership functions.

Abstract: The architecture and implementation of a VLSI chip set that vector quantizes (VQ) image sequences in real time is described. The chip set forms a programmable Single-Instruction, Multiple-Data (SIMD) machine which can implement various vector quantization encoding structures. Its VQ codebook may contain unlimited number of codevectors, N, having dimension up to K = 64. Under a weighted least squared error criterion, the engine locates at video rates the best code vector in full-searched or large tree searched VQ codebooks. The ability to manipulate tree structured codebooks, coupled with parallelism and pipelining, permits searches in as short as O (log N) cycles. A full codebook search results in O(N) performance, compared to O(KN) for a Single-Instruction, Single-Data (SISD) machine. With this VLSI chip set, an entire video code can be built on a single board that permits realtime experimentation with very large codebooks.

Abstract: The author proposed a learning rule for a single-layer network of modules representing adaptive tables of the type formed by T. Kohonen's vector quantization algorithm (Rep. TKK-F-A601, Helsinki Univ. of Technol., 1986). The learning rule allows combination of several modules to learn more complicated functions on higher dimensional spaces. During learning each module learns a function, which is adjusted such as to minimize the average square error between the correct function and the function represented by the network. Although this is a single-layer system, the capability of each module to learn an arbitrary nonlinearity gives the system far more flexibility than a perceptron. At the same time, for output nonlinearities that are a product or a sum of monotonous functions of their arguments there is a unique minimum to which the system is guaranteed to converge. >

Abstract: An interframe hierarchical vector quantizer (IHVQ) is presented that is capable of encoding image sequence scenes at rates below 0.3 bit per pixel per frame. A regular decomposition quadtree method is used to segment the interframe differential signal into homogeneous regions of different block size. Small blocks representing high contrast moving boundaries (i.e., the impulsive component of the difference signal) are vector quantized, whereas large blocks typically representing smooth regions of the image are encoded by the local sample mean of the region. The IHVQ system has a signal-to-noise ratio (SNR) at least 2 dB higher than the SNR of the interframe mean-reconstructed quadtree coding system.

Abstract: Method of and arrangement for image data compression by vector quantization in accordance with a precoding in blocks, thereafter comparing by means of a neural network precoded blocks with reference words stored in the form of a code book so as to transmit selected indices to a receiver. In accordance with the method, the neural network effects a learning phase with prescribed prototypes, thereafter with the aid of test vectors originating from the image generates an adaptive code book which is transmitted to the receiver. This adaptation utilizes attractors, which may be induced metastable states, of the neural network, and which are submitted to an optimizing procedure. The arrangement can process images with a view to their storage. It is also possible to utilize two devices which operate alternately, one device for generating the adaptive code book and the other one to utilize it with the object of processing television pictures in real time.

Abstract: Performance analysis of non-orthogonal block designs for Fh/MFSK Systems under partial band interference.- Probability of error comparison of linear and iterative multiuser detectors.- Recent progress in Multiuser Detection.- Minimax causal transmission of Gaussian stochastic processes over channels subject to correlated jamming.- Efficient MSK spread-spectrum signaling.- On parameter estimation in DS/SSMA formats.- Orthogonal signalling and diversity in partial-band interference.- Applications of robustness measures in signal detection.- Robust multiple hypothesis tests.- Detecting a transient signal by bispectral analysis.- An important pathology of finite dimensional approximations of statistical estimators.- Counterexamples in detection and estimation.- On the convergence of the projection method for an autoregressive process and a matched DPCM code.- Tree-structured vector quantization for progressive transmission image coding.- Path map symbol release algorithms and the exponential metric tree.- Structure simplification of 2-D digital filters: An overview.- Factorization method for inherently stable 2-D recursive digital filters.- A design technique for variable 2-D recursive digital filters.- Analytical methods for the design of 2-D elliptically symmetric digital filters of arbitrary orientation using generalized McClellan transformation.- An efficient algorithm for the design of circular symmetric linear phase recursive digital filters with separable denominator transfer function.- A simulation study of near- and far-end crosstalk cancellation for multi-channel data transmission.- Analysis of a class of adaptive nonlinear predictors.- Recursive arma parameter estimation with a discerning update strategy-finite precision effects.- Analysis of a Fast Quasi-Newton adaptive filtering algorithm.- Adaptive stack filtering under the mean absolute error criterion.- Three-dimensional image reconstruction from scattering data.- A tomographic formulation of bistatic synthetic aperture radar.- Phase retrieval by optimal weighted norm extrapolation.- Reconstruction of high resolution image from noise undersampled frames.- Reconstruction of continuous-tone from halftone by projections onto convex sets.- Design of two-dimensional FIR digital filters by using the singular-value decomposition.- Geometric measures of robustness in signal processing.- State-dependent routing for a multi-service network.- Estimation of the parameters of a second order nonlinear system.

Abstract: A method for compressing data employing vector quantization is achieved by calculating the norm of an input vector and identifying a reference codebook vector which has a norm which is closest to the norm of the input vector. The distance between the input vector and the reference codebook vector selected is computed and employed to identify a vector space about the reference vector containing a subset of codebook vectors one or more of which may be closer to the input vector than the initially selected reference vector. The closest codebook vector is selected iteratively without the necessity of searching every vector in the codebook.

Abstract: A recently developed technique for variable-rate vector quantizer (VQ) design by P.A. Chou et al. (see IEEE Trans. Inf. Theory, vol.35, no.2, p.299-315, 1989) has been applied to both memoryless and predictive VQ of images. This technique, called pruned tree-structured vector quantization (PTSVQ), uses variable-depth encoders that are tree-structured and thus have very low design and search complexity. PTSVQ is applied to a series of medical images, and gains over full-search VQ of up to 3.78 dB in the signal-to-noise-ratio (SNR) are measured. On still images from the USC database, gains of up to 1.63 dB in the peak SNR are realized for predictive PTSVQ over predictive full search VQ, resulting in high image quality at 0.51 bits per pixel. >

Abstract: The authors compare the Y. Linde, A. Buzo, and R.M. Gray vector quantization algorithm (1980) with the frequency-sensitive competitive learning neural network. Each of these techniques is applied to two images, and the distortion and SNR are measured for various size codebooks. The results show that the neural network technique of designing codebooks yields results that are very close to the optimal design. Multiple images are included to show the results of quantization for various bit rates. >

Abstract: The authors present a polynomial-time codeword-mapping algorithm which seeks to minimize the Euclidean distance between all pairs of codewords with a relative Hamming distance of 1, permitting the robust performance of vector quantizations in noisy channels, without a sacrifice in coding bandwidth or quantizer performance. The algorithm is based upon network design considerations, and useful gains of several decibels can be obtained in the error distortion by using the new codeword mapping, without a sacrifice in coding bandwidth or quantizer performance. Results with application to image coding are given, and it is also shown that some natural codes are good robust codes under selected conditions. >

Abstract: The authors investigate the application of several lattice vector quantizers, namely D/sub N/ for N >

Abstract: The authors extend the A-VQ (address-vector quantization) coding technique to encode RGB (red, green, blue) color images by utilizing the interblock and intercolor correlation. A modified A-VQ technique called dynamic address-vector quantization (DA-VQ) is introduced for encoding of color images. A multilayered address vector quantizer is also introduced, where the code vectors at each layer represent the most probable address combinations of the entries of the address codebook at the previous lower layer. Experimental results show reconstructed images at bit rates of 0.5-0.6 bit per pixel with SNR (signal/noise ratio)=28-31 dB. The resulting bit rate is less than that of a standard VQ coding technique by at least a factor of two. >

Abstract: In a quantizer of the invention, a quantization distortion in the case where the optimum vector code word was used and a quantization distortion in the case where the optimum predictive error vector code word was used, are compared by comparing means, thereby selecting which one of the conventional vector quantization and the predictive error vector quantization should be executed for the present input vector. On the other hand, an inverse-quantizer selects which one of the inverse-quantizations should be executed on the basis of the input code number from the vector code. According to the invention, further, the quantizer and inverse-quantizer have the same analyzing means and converting means and execute the adaptation of the code tables by using the quantization results. Thus, the adaptation of the code table of the quantizer and inverse-quantizer can be accomplished without, particularly, adding the information transmitting process for adaptation. On the other hand, by executing the quantization by selectively using the predictive error vector quantizing means, the accuracy of the quantization result is improved and the adaptation of good code tables is realized.