Gain-shape Vector Quantization Research Articles

Logarithmic Pyramid Vector Quantization—Design and Theoretical Analysis

Vector quantization is an integral part of modern speech and audio codecs. This study proposes the logarithmic pyramid vector quantizer (LPVQ), which is a gain-shape vector quantizer specifically designed for the quantization of Laplace distributed memoryless sources. The objective of the study is a theoretical analysis of the LPVQ: We determine the distortion of the shape quantizer with respect to rate and vector dimension for the quantization of an i.i.d. Laplace source. Furthermore, we derive formulas for the quantization signal-to-noise ratio (SNR) of the shape quantizer and the quantization SNR of the LPVQ, giving reliable results for an effective bit rate per vector coordinate of 2bits and higher. We study the SNR-behavior of the LPVQ for infinite dimensions and compare it with the maximal achievable SNR according to the rate-distortion bound. After having proposed a strategy for the allocation of the bit rate for the gain quantization and the quantization of the shape vector, respectively, we verify the derived formulas by simulations.

An Analysis and Application of Fast Nonnegative Orthogonal Matching Pursuit for Image Categorization in Deep Networks

Nonnegative orthogonal matching pursuit (NOMP) has been proven to be a more stable encoder for unsupervised sparse representation learning. However, previous research has shown that NOMP is suboptimal in terms of computational cost, as the coefficients selection and refinement using nonnegative least squares (NNLS) have been divided into two separate steps. It is found that this problem severely reduces the efficiency of encoding for large-scale image patches. In this work, we study fast nonnegative OMP (FNOMP) as an efficient encoder which can be accelerated by the implementation ofQRfactorization and iterations of coefficients in deep networks for full-size image categorization task. It is analyzed and demonstrated that using relatively simple gain-shape vector quantization for training dictionary, FNOMP not only performs more efficiently than NOMP for encoding but also significantly improves the classification accuracy compared to OMP based algorithm. In addition, FNOMP based algorithm is superior to other state-of-the-art methods on several publicly available benchmarks, that is, Oxford Flowers, UIUC-Sports, and Caltech101.

Greedy sparse decompositions: a comparative study

The purpose of this article is to present a comparative study of sparse greedy algorithms that were separately introduced in speech and audio research communities. It is particularly shown that the Matching Pursuit (MP) family of algorithms (MP, OMP, and OOMP) are equivalent to multi-stage gain-shape vector quantization algorithms previously designed for speech signals coding. These algorithms are comparatively evaluated and their merits in terms of trade-off between complexity and performances are discussed. This article is completed by the introduction of the novel methods that take their inspiration from this unified view and recent study in audio sparse decomposition.

Beat-Based ECG Compression Using Gain-Shape Vector Quantization

An electrocardiogram (ECG) data compression scheme is presented using the gain-shape vector quantization. The proposed approach utilizes the fact that ECG signals generally show redundancy among adjacent heartbeats and adjacent samples. An ECG signal is QRS detected and segmented according to the detected fiducial points. The segmented heartbeats are vector quantized, and the residual signals are calculated and encoded using the AREA algorithm. The experimental results show that with the proposed method both visual quality and the objective quality are excellent even in low bit rates. An average PRD of 5.97% at 127 b/s is obtained for the entire 48 records in the MIT-BIH database. The proposed method also outperforms others for the same test dataset.

Encoding of multispectral and hyperspectral image data using wavelet transform and gain shape vector quantization

An effective and lossy compression technique for multispectral and hyperspectral image data minimizes both the spatial and spectral correlations while preserving the spectral characteristics of the data. In this paper, we combine wavelet transform and a variant of vector quantization for decorrelating both spatial and spectral information, and thus aim to achieve superior quality. We use 2-D wavelet transform followed by Kronecker-Product Gain-Shape Vector Quantization. This is coupled with the generalized BFOS for obtaining an optimal bit-rate. The pixels within the subbands of multi- and hyper-spectral images exhibit greater spectral redundancy which is thus exploited by designing multiresolution codebooks. Results are presented for multispectral and hyperspectral data taken from different sensors in different bands. The results obtained with our scheme are compared with other techniques designed for multi-/hyper-spectral image data and the Wavelet-based JPEG-2000. The computational requirement of the proposed technique is lower in comparison with other vector-quantization techniques.

The atoms of vision: Cartesian or polar?

The inherent structure of the encoding in early stages of the visual system is investigated from a combined information-theoretical, psychophysical, and neurophysiological perspective. We argue that the classical modeling in terms of linear spatial filters is equivalent to the assumption of a Cartesian organization of the feature space of early vision. We show that such a linear Cartesian feature space would be suboptimal for the exploitation of the statistical redundancies of natural images since these have a radially separable probability-density function. Therefore a more efficient representation can be obtained by a nonlinear encoding that yields a feature space with polar organization. This prediction of the information-theoretical approach regarding the organization of the feature space of early vision is confirmed by our psychophysical measurements of basic discrimination capabilities for elementary Gabor patches, and the necessary nonlinear operations are shown to be closely related to cortical gain control and to the phase invariance of complex cells. Finally, we point out some striking similarities between the polar representation in visual cortex and basic image-coding strategies pursued in shape-gain vector quantization schemes.

A MS-GS VQ codebook design for wireless image communication using genetic algorithms

An image compression technique is proposed that attempts to achieve both robustness to transmission bit errors common to wireless image communication, as well as sufficient visual quality of the reconstructed images. Error robustness is achieved by using biorthogonal wavelet subband image coding with multistage gain-shape vector quantization (MS-GS VQ) which uses three stages of signal decomposition in an attempt to reduce the effect of transmission bit errors by distributing image information among many blocks. Good visual quality of the reconstructed images is obtained by applying genetic algorithms (GAs) to codebook generation to produce reconstruction capabilities that are superior to the conventional techniques. The proposed decomposition scheme also supports the use of GAs because decomposition reduces the problem size. Some simulations for evaluating the performance of the proposed coding scheme on both transmission bit errors and distortions of the reconstructed images are performed. Simulation results show that the proposed MS-GS VQ with good codebooks designed by GAs provides not only better robustness to transmission bit errors but also higher peak signal-to-noise ratio even under high bit error rate conditions.

Kronecker-product gain-shape vector quantization for multispectral and hyperspectral image coding

This paper proposes a new vector quantization based (VQ-based) technique for very low bit rate encoding of multispectral images. We rely on the assumption that the shape of a generic spatial block does not change significantly from band to band, as is the case for high spectral-resolution imagery. In such a hypothesis, it is possible to accurately quantize a three-dimensional (3-D) block-composed of homologous two-dimensional (2-D) blocks drawn from several bands-as the Kronecker-product of a spatial-shape codevector and a spectral-gain codevector, with significant computation saving with respect to straight VQ. An even higher complexity reduction is obtained by representing each 3-D block in its minimum-square-error Kronecker-product form and by quantizing the component shape and gain vectors. For the block sizes considered, this encoding strategy is over 100 times more computationally efficient than unconstrained VQ, and over ten times more computationally efficient than direct gain-shape VQ. The proposed technique is obviously suboptimal with respect to VQ, but the huge complexity reduction allows one to use much larger blocks than usual and to better exploit both the statistical and psychovisual redundancy of the image. Numerical experiments show fully satisfactory results whenever the shape-invariance hypothesis turns out to be accurate enough, as in the case of hyperspectral images. In particular, for a given level of complexity and image quality, the compression ratio is up to five times larger than that provided by ordinary VQ, and also larger than that provided by other techniques specifically designed for multispectral image coding.

Rotated Barnes-Wall lattice based vector quantizer and its application in image-sequence coding

A new scheme is presented to design a rotated Barnes-Wall lattice based vector quantizer(LVQ). The construction method of the LVQ and its, fast quantizing algorithm are described at first. Then gain-shape lattice vector quantizer (GSLVQ) with LVQ as shape quantizer is discussed. Finally the GSLVQ is used in image-sequence coding and good experimental results are obtained.

Perceptually based directional classified gain-shape vector quantization

A new image coding system, termed directional classified gain-shape vector quantization (DCGSVQ), is introduced in this paper. A content-classifier, operating in the spatial domain, is employed to classify each image block of 8/spl times/8 pixels into one of several classes which represent various image patterns (edges in various directions, monotone areas, complex texture, etc.). Then a classified gain-shape vector quantizer is employed in the cosine domain to encode directional vectors of AC transform coefficients while using either a scalar quantizer or a gain-shape vector quantizer to encode the DC coefficients. A new vector configuration scheme is proposed in order to better adapt the system to the local statistics of the image blocks. In addition, various properties of the human visual system like frequency sensitivity, the masking effect, and orientation sensitivity are incorporated into the proposed system to improve further the subjective quality of the reconstructed images. A new algorithm for designing the various shape codebooks, needed for the DCGSVQ, is proposed based on the classified nearest neighbor clustering (CNNC) algorithm of Kubrick and Ellis (1990). Finally, an optional simple method for feature enhancement, based on inherent properties of the proposed system, is proposed enabling further image processing at the receiver. Coding results are presented showing a very good subjective quality of reconstructed images for bit-rates in the range 0.48-0.625 b per pixel. >

Concentric-shell partition vector quantization with application to image coding

A method for designing a vector quantizer by first partitioning the residual image vector space into concentric shells and then searching for the smallest possible codebook to represent the residual image vector space, while adhering to the visual perceptive qualities such as edges and textures in the image representation, is described. The coding method involves the decomposition of the image vector into relatively independent components, each with a small dynamic range, to permit the design of a small fixed codebook for the vector quantizer. Optimal partitioning amounts to optimally selecting the set of shell radii, which is achieved using a modified form of simulated annealing. The results obtained in the coding of images show that the concentric-shell partition vector quantizer compares favourably with the gain-shape vector quantizer in terms of subjective image quality at the same bit rate while achieving higher SNR and lower computational complexity. >

Shape-gain vector quantization for noisy channels with applications to image coding

A new design procedure for shape-gain vector quantizers (SGVQs) which leads to substantially improved robustness against channel errors without increasing the computational complexity is proposed. This aim is achieved by including the channel transition probabilities in the design procedure, leading to an improved assignment of binary codewords to the coding regions as well as a change of partition and centroids. In contrast to conventional design, negative gain values are also permitted. The new design procedure is applied to adaptive transform image coding. Simulation results are compared with those obtained by the conventional design procedure. The new algorithm is particularly useful for heavily distorted or fading channels.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>