A Hybrid Vector Quantization Combining a Tree Structure and a Voronoi Diagram

The authors study codeword index assignment to allow for progressive image transmission of fixed rate full-search vector quantization (VQ). They develop three new methods of assigning indices to a vector quantization codebook and formulate these assignments as labels of nodes of a full-search progressive transmission tree. The tree is used to design intermediate codewords for the decoder so that full-search VQ has a successive approximation character. The binary representation for the path through the tree represents the progressive transmission code. The methods of designing the tree that they apply are the generalized Lloyd algorithm, minimum cost perfect matching from optimization theory, and a method of principal component partitioning. Their empirical results show that the final method gives intermediate signal-to-noise ratios (SNRs) that are close to those obtained with tree-structured vector quantization, yet they have higher final SNRs.

The authors examined vector quantizer performance as a function of training sequence size for tree-structured and full-search vector quantizers. The performance was measured by the mean-squared error between the input image and the quantizer output at a given bit rate. The training sequence size was measured either by the number of training images, or by the number of training vectors. When the training vectors were counted, they were selected randomly from among the training images. For every training sequence size, vector quantizers were developed from several different training sequences, and the distortion was calculated for different test sequences in a cross validation procedure. Preliminary results suggest that plots of distortion vs. number of training images follow an algebraic decay, as expected from analogous results of learning theory. >

This correspondence discusses a progressive vector quantization (VQ) compression approach, which decomposes image data into a number of levels using full-search VQ. The final level is losslessly compressed, enabling lossless reconstruction. The computational difficulties are addressed by implementation on a massively parallel SIMD machine. We demonstrate progressive VQ on multispectral imagery obtained from the advanced very high resolution radiometer (AVHRR) and other earth-observation image data, and investigate the tradeoffs in selecting the number of decomposition levels and codebook training method.

Stochastic reservoir models generate large grids, sometimes in excess of millions of cells. These models need to be upscaled to reduce the number of grid blocks for practical flow simulations. As a consequence, the volumes of the upscaled simulation grids are represented by corresponding coarser values. This may result in a detrimental correlation structure and variance which may be different from that obtained from the fine grid. Various upscaling algorithms have been proposed, ranging from simple averaging to conservation of fluid flux, and more recently, wavelet transforms. These algorithms are principally focused towards upscaling tensorial reservoir properties such as permeability. Scalar properties, such as porosity, are generally volume-averaged. This approach of alienating porosity from permeability for upscaling purposes questions the geological underpinnings of the depositional/diagenetic model being upscaled. In this paper, we propose a completely new perspective to address the issue of upscaling: Neural Vector Quantization. This new approach offers opportunities such as multivariate upscaling where many reservoir properties can be upscaled simultaneously. Neural Vector Quantization (NVQ) is used to achieve data compression in vector spaces. In NVQ upscaling the components of the input vector are the different reservoir properties (permeability, porosity, water saturation) to be upscaled simultaneously. The purpose of vector quantization is to categorize a given set, or a distribution of input vectors, into several clusters called Voronoi tessellations. Input vectors in the same Voronoi tessellation are considered to be similar and fall into the same cluster. The vector corresponding to the centroid of the tessellation is the globally averaged value of all the input vectors in that Voronoi tessellation. This vector is called the reference vector. The reference vector yields the upscaled values of the physical properties of interest. In this study, we achieve vector quantization using a new self-organizing, competitive-clustering, adaptive-structure neural network algorithm. Since we have specifically designed this algorithm for petroleum engineering applications, it performs clustering on highly-disjointed datasets. We call it the Heterogeneous Space Classifier (HSC) algorithm. We tested HSC on a 25x25x4 three-phase, black-oil model. The model contained one injector and one producer. We compared the reservoir performance for the upscaled and fine grids by evaluating the average reservoir pressure, cumulative production, and fluid flowrates for 10 years. We upscaled the model to a 10x10x4 grid without compromising the flow behavior of the system. Introduction Constrained models have dominated recent efforts in reservoir modeling. Some of the initial studies concentrated on automatic history-matching algorithms, which result in pseudoization of reservoir properties, especially the relative permeabilities. Such methods were severely criticized by petrophysicists and geologists since the final "pseudo" property did not honor the experimentally measured value. In the past decade, the emphasis shifted to building spatially-descriptive models by honoring the point-data as well as the inherent correlation structures observed between the point-located data. These geostatistical techniques, constrained to 3D seismic or well-test data, can yield geologically consistent models. Some of these models have fine geological descriptions built into the model through iterative interaction between the geologist, the geophysicist, and the reservoir engineer. Nowadays, models containing geological entities, such as braided channels and alluvial fans, are commonly encountered in reservoir simulation literature. These beautifully detailed models capture the depositional and diagenetic nuances of the reservoir, but from a simulation standpoint, they demand a prohibitive number of simulation cells. Constrained, stochastic models can frequently exceed a million cells. Although impressive, current computing technology limits us in simulating million-cell models. In fact, the routine demands simulation of grids that are one order lower in magnitude. This requires a translation of the detailed grids to a coarser, albeit a more manageable, level without sacrificing the anticipated reservoir performance. This translation is commonly known as upscaling. P. 137^

Region-based compression technique is particularly useful for radiological archiving system as it allows diagnostically important regions to be compressed with near lossless quality while the non-diagnostically important regions (NROI) to be compressed at lossy quality. In this paper, we present a region-based compression technique tailored for MRI brain scans. In the proposed technique termed as automated arbitrary PCA (AAPCA), an automatic segmentation based on brain symmetrical property is used to separate the ROI from the background. The arbitrary-shape ROI is then compressed by block-to-row PCA algorithm (BTRPCA) based on a factorization approach. The ROI is optimally compressed with lower compression rate while the NROI is compressed with higher compression rate. The proposed technique achieves satisfactory segmentation performance. The subjective and objective evaluation performed confirmed that the proposed technique achieves better performance metrics (PSNR and CoC) and higher overall compression rate. The experimental results also demonstrated that the proposed technique is more superior to various state-of-the-art compression methods.

Vector Quantisation (VQ) is an efficient coding algorithm that has been widely used in the field of video and image coding, due to its fast decoding efficiency. However, the indexes of VQ are sometimes lost because of signal interference during the transmission. In this paper, we propose an efficient estimation method to conceal and recover the lost indexes on the decoder side, to avoid re-transmitting the whole image again. If the image or video has the limitation of a period of validity, re-transmitting the data wastes the resources of time and network bandwidth. Therefore, using the originally received correct data to estimate and recover the lost data is efficient in time-constrained situations, such as network conferencing or mobile transmissions. In nature images, the pixels are correlated with their neighbours and VQ partitions the image into sub-blocks and quantises them to the indexes that are transmitted; the correlation between adjacent indexes is very strong. There are two parts of the proposed method. The first is pre-processing and the second is an estimation process. In pre-processing, we modify the order of code- vectors in the VQ codebook to increase the correlation among the neighbouring vectors. We then use a special filtering method in the estimation process. Using conventional VQ to compress the Lena image and transmit it without any loss of index can achieve a PSNR of 30.429 dB on the decoder. The simulation results demonstrate that our method can estimate the indexes to achieve PSNR values of 29.084 and 28.327 dB when the loss rate is 0.5% and 1%, respectively.

Purpose In recent years, principal component analysis (PCA) has attracted great attention in dimension reduction. However, since a very large transformation matrix must be used for reconstructing the original data, PCA has not been successfully applied to image compression. To solve this problem, this paper aims to propose a new technique called k-PCA. Design/methodology/approach Actually, k-PCA is a combination of vector quantization (VQ) and PCA. The basic idea is to divide the problem space into k clusters using VQ, and then find a PCA encoder for each cluster. The point is that if the k-PCA encoder is obtained using data containing enough information, it can be used as a semi-universal encoder to compress all images in a given domain. Findings Although a k-PCA encoder is more complex than a single PCA encoder, the compression ratio can be much higher because the transformation matrices can be excluded from the encoded data. The performance of the k-PCA encoder can be improved further through learning. For this purpose, this paper-proposes an extended LBG algorithm. Originality/value The effectiveness of the k-PCA is demonstrated through experiments with several well-known test images.

An Image Sequence Coder Based on Vector Quantization and Progressive Transmission

We propose an improvement to VQ by applying data and dimensionality reduction techniques on the original dataset and using different resolutions generated by the reduction techniques as input to the GLA with splitting at different stages of codebook generation. The different resolutions are pre-computed (a one time cost), and are used instead of the original dataset in each iteration of the GLA. We propose three variants of the reduced data representation VQ (RDR- VQ) based on the three reduced data representation techniques we use: 1. Reduced precision VQ (RP-VQ), where we use a simple rounding off of precision of the original dataset; 2. Wavelet RDR-VQ, where we use a discrete wavelet transform of the original dataset 3. PCA RDR-VQ, where we use a linear transform of the original dataset using PCA The difference in our work with existing algorithms that use VQ with wavelets is while these algorithms use multiple quantizers on the wavelet subbands, our method uses the different subbands as input to different iterations of a single quantizer. Different resolutions of the dataset are used as input for the different Lloyd iterations. An important consideration is choosing an appropriate resolution level for each of these iterations. We call the different resolution levels used by the algorithm to compute the final codebook a resolution sequence.

In this paper, we propose a data embedding method into still images based on Vector Quantization (VQ). In recent years, several VQ-based data embedding methods have been proposed. For example, `Mean Gray-Level Embedding method (MGLE)' are `Pair wise Nearest-Neighbor Embedding method (PNNE)' are simple, but not sufficiently effective. Meanwhile, an efficient adaptive data hiding method called `Adaptive Clustering Embedding method (ACE)' was proposed, but is somewhat complicated because the VQ indices have to be adaptively clustered in the embedding process. In our proposed method, output vectors are considered as nodes, and nodes are linked as a tree structure and information is embedded by using some of linked vectors. The simulation results show that our proposed method indicates higher SNR than the conventional methods under the same amounts of embedded data.

An image that is mapped into a bit stream suitable for communication over or storage in a digital medium is said to have been compressed. Using tree-structured vector quantizers (TSVQs) is an approach to image compression in which clustering algorithms are combined with ideas from tree-structured classification to provide code books that can be searched quickly and simply. The overall goal is to optimize the quality of the compressed image subject to a constraint on the communication or storage capacity, i.e. on the allowed bit rate. General goals of image compression and vector quantization are summarized in this paper. There is discussion of methods for code book design, particularly the generalized Lloyd algorithm for clustering, and methods for splitting and pruning that have been extended from the design of classification trees to TSVQs. The resulting codes, called pruned TSVQs, are of variable rate, and yield lower distortion than fixed-rate, full-search vector quantizers for a given average bit rate. They have simple encoders and a natural successive approximation (progressive) property. Applications of pruned TSVQs are discussed, particularly compressing computerized tomography images. In this work, the key issue is not merely the subjective attractiveness of the compressed image but rather whether the diagnostic accuracy is adversely aflected by compression. In recent work, TSVQs have been combined with other types of image processing, including segmentation and enhancement. The relationship between vector quantizer performance and the size of the training sequence used to design the code and other asymptotic properties of the codes are discussed.

Image vector quantization codec indices recovery using Lagrange interpolation

The process to minimize the total number of bits required to depict an image is known as image compression. The main goal of image compression is to minimize the transmission cost and to reduce the storage space. Vector quantization is a most popular technique for lossy compression due to its high compression rate and simple decoding algorithm. The key technique of VQ is the codebook design. In this paper, we have compared and found out the compression ratios of jpg and tiff images using VQ for lossy compression and k-means clustering.

Vector quantization and fuzzy ranks for image reconstruction

The emergence of mobile cloud computing indicates that abundant applications such as mobile games are available. Clouds have many interesting characteristics including on demand service, measured service, scalable elastic service, “anytime, anywhere” network access in cloud networks. Benefit due to the service controlled by communication between objects is now being increased by people who use these services in real life. In a very large scale mobile gaming environment with limited wireless network bandwidth, the command that game users give should be reflected to the game immediately and should be transferred to several objects at once, and it takes a certain amount of time to get the command pass to other users. An efficient mechanisms for state update are crucial to allow graceful real time interaction for many players and limited network bandwidth. Therefore, we propose a scheme for an optimized state update based on event locking and analytical models for mobile game in this paper. We design and implement the gaming server applying to our proposed scheme. The experimental results show that the proposed scheme can effectively improve the performance for mobile games and reduce communication overhead in cloud networks.