Finite-state Vector Quantization Research Articles

Finite-State Vector Quantization Techniques for Image Compression

Finite-State Vector Quantization Techniques for Image Compression

A memory efficient finite-state source coding algorithm for audio MDCT coefficients

To achieve a better trade-off between the vector dimension and the memory requirements of a vector quantizer (VQ), an entropy-constrained VQ (ECVQ) scheme with finite memory, called finite-state ECVQ (FS-ECVQ), is presented in this paper. The scheme consists of a finite-state VQ (FSVQ) and multiple component ECVQs. By utilizing the FSVQ, the inter-frame dependencies within source sequence can be effectively exploited and no side information needs to be transmitted. By employing the ECVQs, the total memory requirements of the FS-ECVQ can be efficiently decreased while the coding performance is improved. An FS-ECVQ, designed for the modified discrete cosine transform (MDCT) coefficients coding, was implemented and evaluated based on the Unified Speech and Audio Coding (USAC) scheme. Results showed that the FS-ECVQ achieved a reduction of the total memory requirements by about 11.3%, compared with the encoder in USAC final version (FINAL), while maintaining a similar coding performance.

Research on Channel Quantization Algorithm of Time Correlated Channels

Focusing on time correlation of real communication channels, a channel quantization algorithm based on finite state vector quantization (FSVQ) is proposed. Firstly channels are partitioned into finite states, then codebooks corresponding to each state are constructed, which are used to quantize channels transferred from corresponding states. Further, the state transition function is designed to ensure the synchronization between transmitter and receiver. The proposed algorithm can achieve improved performance with the same feedback load compared with classical memoryless channel quantizer without consideration of the influence of time correlation. Simulation results verify the effectiveness of the proposed algorithm.

Feedback Quantization for Linear Precoded Spatial Multiplexing

This paper gives an overview and a comparison of recent feedback quantization schemes for linear precoded spatial multiplexing systems. In addition, feedback compression methods are presented that exploit the time correlation of the channel. These methods can be roughly divided into two classes. The first class tries to minimize the data rate on the feedback link while keeping the performance constant. This class is novel and relies on entropy coding. The second class tries to optimize the performance while using the maximal data rate on the feedback link. This class is presented within the well-developed framework of finite-state vector quantization. Within this class, existing as well as novel methods are presented and compared.

New variable-rate finite state vector quantizer for image coding

Although side-match vector quantization (SMVQ) and its variants have been proposed to reduce the bit rate of coding images, the coding quality is decreased by it. The reason is that when a block is encoded in SMVQ, the side-match method uses only two neighboring blocks, (no edge information is available in the other two neighboring blocks) to predict the state of the codebook. We propose a new variable-rate finite state vector quantizer (VRFSVQ) to encode the blocks with a variable rate according to both the coding quality and the bit rate. The VRFSVQ can preencode all the blocks, allowing each block to employ more than two neighboring blocks to yield the state codebook. Furthermore, whereas users of SMVQ must specify the size of the state codebook before applying the side-match method to yield the state codebook, in the VRFSVQ the users do not need to specify the size of the state codebook for each encoding block. Experimental results indicate that the VRFSVQ has a high peak SNR and low bit rate for image coding.

On Finite-State Vector Quantization for Noisy Channels

Finite-state vector quantization (FSVQ) over a noisy channel is studied. A major drawback of a finite-state decoder is its inability to track the encoder in the presence of channel noise. In order to overcome this problem, we propose a nontracking decoder which directly estimates the code vectors used by a finite-state encoder. The design of channel-matched finite-state vector quantizers for noisy channels, using an iterative scheme resembling the generalized Lloyd algorithm, is also investigated. Simulation results based on encoding a Gauss-Markov source over a memoryless Gaussian channel show that the proposed decoder exhibits graceful degradation of performance with increasing channel noise, as compared with a finite-state decoder. Also, the channel-matched finite-state vector quantizers are shown to outperform channel-optimized vector quantizers having the same vector dimension and rate. However, the nontracking decoder used in the channel-matched finite-state quantizer has a higher computational complexity, compared with a channel-optimized vector-quantizer decoder. Thus, if they are allowed to have the same overall complexity (encoding and decoding), the channel-optimized vector quantizer can use a longer encoding delay and achieve similar or better performance. Finally, an example of using the channel-matched finite-state quantizer as a backward-adaptive quantizer for nonstationary signals is also presented.

Adaptive initial blocks for improving gradient-match and side-match vector quantization of images

The selection of initial blocks is one of the important issues in finite-state vector quantizers (FSVQs) for images. Conventional FSVQs use blocks located at fixed positions as initial blocks, which then are coded by the codewords in the super codebook. We propose an adaptive-initial-block (AIB) scheme to determine the initial blocks for gradient-match (GM) and side-match (SM) vector quantizers, which are two significant classes of FSVQs. According to the next-state functions used in GMVQs and SMVQs, the blocks with large boundary matching errors in original VQs are selected as the initial blocks. The error propagation effects can be reduced, and the coding performance is significantly improved. The simulation results show that the peak signal-to-noise ratios of coded images can be 2 dB higher than that of conventional GMVQs and SMVQs when the state codebook sizes are much smaller than that of the super codebook.

Jigsaw-puzzle vector quantization for image compression

A new finite-state vector quantization scheme called jigsaw-puzzle vector quantization (JPVQ) is proposed to provide better image quality, especially in the low bit rate context. For low bit rate image coding with conventional finite-state vector quantization (FSVQ) techniques, image quality degrades due to error propagation from one state to the next. The proposed JPVQ algorithm exploits the four-step side-match prediction technique to optimize the spatial continuity of each encoded block to improve the coding performance and reduce the error propagation effect. In the proposed coding scheme, an input block can be encoded by the jigsaw-puzzle block, the dynamic codebook, or the super-codebook. It is demonstrated with experimental results that JPVQ performs significantly better than traditional FSVQ techniques.

A New Side-Match Finite-State Vector Quantization Using Neural Networks for Image Coding

The side-match finite-state vector quantization (SMVQ) schemes improve performance over the vector quantization by exploiting the neighboring vector correlations within the image. In this paper, we propose a neural network side-match finite-state vector quantization (NN-SMVQ) scheme that combines the techniques of neural network prediction and the SMVQ coding method. In our coding scheme, the multilayer perceptron network is used to improve the accuracy of side-match prediction by utilizing the property of the neural network nonlinear prediction. The NN-SMVQ scheme not only has the advantages of the SMVQ scheme but also improves the coded image quality. Experimental results are given and comparisons are made using our NN-SMVQ coding scheme and some other coding techniques. In the experiments, our NN-SMVQ coding scheme achieves the better visual quality about edge region and the best PSNR performance at nearly the same bit rate. This new NN-SMVQ scheme is also simple and efficient for the hardware design. Moreover, the new scheme does not adversely affect other useful functions provided by the conventional SMVQ scheme.

Tree-Structured Index Grouping Algorithm for Lossless Coding of VQ Index Map

In this paper, a new algorithm is proposed for removing the spatial redundancy of the index values of the codevectors after encoding the image using Vector Quantization. This algorithm, called the Tree-Structured Index Grouping algorithm (TSIG), employs a combination of multipath search and the Index Grouping algorithm to encode the index map in a lossless fashion. After each search, based on the index values occurred in the search path, a particular bit pattern is transmitted. The performance of this algorithm is investigated on still 8-bit grayscale images and compared with the Index Grouping algorithm results. Also, a Finite State Vector Quantization (FSVQ) reordering procedure for selecting the subcodebook is investigated and the performance of the encoder is measured in terms of BPP, PSNR and encoding time. Further, to improve the performance of the algorithm, a combination of FSVQ and TSIG algorithm is proposed.

Gradient match vector quantizers for images

We propose a new class of finite-state vector quantizers (FSVQs), called gradient match vector quantizers (GMVQs), in the im- age coding framework. GMVQs can be considered more general than previously proposed side match vector quantizers (SMVQs) since more border pixels between two neighboring blocks are considered in the state codebook design. Moreover, the concept of gradient matching used in GMVQs can be adjoined to another previously proposed overlap match vector quantizers (OMVQs). Thus another new class of FSVQs are pro- posed and named as gradient and overlap match vector quantizers (GOMVQs). GMVQs and GOMVQs utilize the 2-D spatial continuity of the pixel gradient as well as the high spatial correlation of pixels in typical grayscale images. Both minimize the gradient errors of the border pixels between blocks in ordinary vector quantization of images. In addition to reducing the granular noise that causes the annoying effect of visible pixel block boundaries, the proposed GMVQs and GOMVQs also can preserve the global gradient among the block boundaries and reduces more step noise than SMVQs and OMVQs in the area of high contrast edges. Experiments with the ''Lena'' image show that the proposed GMVQ can achieve the performance superior to those of SMVQ maxi- mum more than 1 dB peak signal-to-noise ratio (PSNR) under the same bit rate. On the other hand, GOMVQs can achieve further bit rate reduc- tion (about 0.14 to 0.3 bit/pixel) than OMVQ using the variable length noiseless code for the channel symbols. © 2000 Society of Photo-Optical Instru- mentation Engineers. (S0091-3286(00)00108-2)

An optimization of finite-state vector quantization for image compression

This paper focuses on the conditional histogram (CH) next-state function design used for the finite-state vector quantization (FSVQ) image compression approach. A new coding scheme is proposed which optimizes the performance of CH while ensuring the same reconstruction quality as that of the full-search VQ. The optimization is performed by determining for every input block the subcodebook size that minimizes the expected value of the number of bits in the compressed bit-flow. Two different algorithms are studied in order to ensure the best reconstruction. The proposed scheme is shown to give better results than classical FSVQ approaches. In fact, the proposed approach reveals the relationship between FSVQ and conditional entropy-coded VQ scheme.

Image Coding Using Adaptive Classified Side-Match Finite-State Vector Quantization

In this article, a new vector quantization (VQ) scheme called adaptive classified side-match finite-state vector quantization (ACSMVQ) is presented. This technique takes advantage of classified vector quantization (CVQ) and side-match vector quantization (SMVQ) so that the compression efficiency is much more attractive than traditional VQ techniques. In ACSMVQ, image blocks are classified into two main classes: edge blocks and non-edge blocks. For improving image quality, non-edge and edge blocks are further reclassified into different classes based on the properties of neighbouring blocks. Kirsh operators are utilized for the detection of edge properties within an image block. In order to synchronize the states in the encoder and decoder, the quantized upper and left blocks are exploited for classifying the input block both in the encoder and decoder. Therefore, no class index needs to be transmitted to the decoder. Moreover, the compression ratio can be further improved by applying small state code book. As shown in the experiment results, the average improvement of ACSMVQ over ordinary SMVQ is up to 2.7 dB at nearly the same bit-rate. Moreover, in comparison with ordinary VQ, the average improvement can be up to 4.24 dB at the same bit-rate.

A new dynamic finite-state vector quantization algorithm for image compression

The picture quality of conventional memory vector quantization techniques is limited by their supercodebooks. This paper presents a new dynamic finite-state vector quantization (DFSVQ) algorithm which provides better quality than the best quality that the supercodebook can offer. The new DFSVQ exploits the global interblock correlation of image blocks instead of local correlation in conventional DFSVQs. For an input block, we search the closest block from the previously encoded data using the side-match technique. The closest block is then used as the prediction of the input block, or used to generate a dynamic codebook. The input block is encoded by the closest block, dynamic codebook or supercodebook. Searching for the closest block from the previously encoded data is equivalent to expand the codevector space; thus the picture quality achieved is not limited by the supercodebook. Experimental results reveal that the new DFSVQ reduces bit rate significantly and provides better visual quality, as compared to the basic VQ and other DFSVQs.

Three-sided side match finite-state vector quantization

Several low bit-rate still-image compression methods have been presented, such as SPHIT, hybrid VQ, and the Wu-Chen (see Proc. IEEE ICASSP, 1997) method. In particular, the image "Lena" can be compressed using less than 0.15 bpp at 31.4 dB or higher. These methods exercise the analysis techniques (wavelet or subband) before distributing the bit rate to each piece of an image, thus the dilemma between bit rate and distortion can be solved. In this paper, we propose a simple but comparable method that adopts the technique of side match VQ only. The side match vector quantization (SMVQ) is an effective VQ coding scheme at low bit-rate. The conventional side match (two-sided) VQ utilizes the codeword information of two neighboring blocks to predict the state codebook of an input vector. We propose a hierarchical three-sided side match finite-state vector quantization (HTSMVQ) method that can: (1) make the state codebook size as small as possible-the size is reduced to one if the prediction can perform perfectly; (2) improve the prediction quality for edge blocks; and (3) regularly refresh the codewords to alleviate the error propagation of side match. In the simulation results, the image "Lena" can be coded with a PSNR 34.682 dB at 0.25 bpp. It is better than SPIHT, EZW, FSSQ and hybrid VQ with 34.1, 33.17, 33.1, and 33.7 dB, respectively. At a bit rate lower than 0.15 bpp, only the enhanced version of EZW performs better than our method, at about 0.14 dB.

Topological surgery encoding improvements based on adaptive bit allocation and DFSVQ

New methods to improve the encoding of the connectivity and geometry of the topological surgery scheme are proposed. In connectivity compression, after obtaining the vertex and triangle spanning trees by decomposing a three-dimensional object, bits are adaptively allocated to each run of two spanning trees on a threshold basis. The threshold is the length of a binary number of the maximum run length. If a run length exceeds the threshold, it is represented by a binary number of the run length. Otherwise, it is represented by a bit sequence. Therefore, compression efficiency is enhanced through an adaptive bit allocation to each run of two spanning trees. In geometry compression, since vertices represented by three-dimensional vectors are stored according to the order of the travelling along vertex spanning tree by depth-first searching, they have geometrical closeness. The geometry compression efficiency can be improved if the local characteristics of vectors are considered. Therefore, dynamic finite state vector quantization, which has subcodebooks depending on a local characteristic of vectors, is used to encode the geometry information. As it dynamically constructs a subcodebook by predicting an input vector's state, it produces less distortion and gives better visual quality than conventional methods.

Speech coding and joint data/channel bias estimation using finite state vector quantizer derived from sequential constraints

A joint data (features) and channel (bias) estimation framework for robust processing of speech received over a channel is described. A trellis encoded vector quantizer is used as a pre-processor to estimate the channel bias using blind maximum likelihood sequence estimation. Sequential constraint in the feature vector sequence of a speech signal is applied for the selection of the quantized signal constellation and for the decoding process in joint data and channel estimation. A two state trellis encoded vector quantizer is designed for signal bias removal applications.

Multiscale video compression using adaptive finite-state vector quantization

We investigate the use of vector quantizers (VQs) with memory to encode image sequences. A multiscale video coding technique using adaptive finite-state vector quantization (FSVQ) is presented. In this technique, a small codebook (subcodebook) is generated for each input vector from a much larger codebook (supercodebook) by the selection (through a reordering procedure) of a set of appropriate codevectors that is the best representative of the input vector. Therefore, the subcodebook dynamically adapts to the characteristics of the motion-compensated frame difference signal. Several reordering procedures are introduced, and their performance is evaluated. In adaptive FSVQ, two different methods, predefined thresholding and rate-distortion cost optimization, are used to decide between the supercodebook and subcodebook for encoding a given input vector. A cache-based vector quantizer, a form of adaptive FSVQ, is also presented for very-low-bit-rate video coding. An efficient bit-allocation strategy using quadtree decomposition is used with the cache-based VQ to compress the video signal. The proposed video codec outperforms H.263 in terms of the peak signal-to-noise ratio and perceptual quality at very low bit rates, ranging from 5 to 20 kbps. The picture quality of the proposed video codec is a significant improvement over previous codecs, in terms of annoying distortions (blocking artifacts and mosquito noises), and is comparable to that of recently developed wavelet-based video codecs. This similarity in picture quality can be explained by the fact that the proposed video codec uses multiscale segmentation and subsequent variable-rate coding, which are conceptually similar to wavelet-based coding techniques. The simplicity of the encoder and decoder of the proposed codec makes it more suitable than waveletbased coding for real-time, very-low-bit-rate video applications. © 1998 SPIE and IS&T. [S1017-9909(98)00204-9]

Constrained-storage vector quantization with a universal codebook

Many image compression techniques require the quantization of multiple vector sources with significantly different distributions. With vector quantization (VQ), these sources are optimally quantized using separate codebooks, which may collectively require an enormous memory space. Since storage is limited in most applications, a convenient way to gracefully trade between performance and storage is needed. Earlier work addressed this problem by clustering the multiple sources into a small number of source groups, where each group shares a codebook. We propose a new solution based on a size-limited universal codebook that can be viewed as the union of overlapping source codebooks. This framework allows each source codebook to consist of any desired subset of the universal code vectors and provides greater design flexibility which improves the storage-constrained performance. A key feature of this approach is that no two sources need be encoded at the same rate. An additional advantage of the proposed method is its close relation to universal, adaptive, finite-state and classified quantization. Necessary conditions for optimality of the universal codebook and the extracted source codebooks are derived. An iterative design algorithm is introduced to obtain a solution satisfying these conditions. Possible applications of the proposed technique are enumerated, and its effectiveness is illustrated for coding of images using finite-state vector quantization, multistage vector quantization, and tree-structured vector quantization.

An on-line universal lossy data compression algorithm via continuous codebook refinement .III. Redundancy analysis

For pt.II see ibid., vol.42, p.822-36 (1996). The Gold-washing data compression algorithm is an adaptive vector quantization algorithm with vector dimension n. In this paper, a redundancy problem of the Gold-washing data compression algorithm is considered. It is demonstrated that for any memoryless source with finite alphabet A and generic distribution p and for any R>0, the redundancy of the Gold-washing data compression algorithm with dimension n (defined as the difference between the average performance of the algorithm and the distortion-rate function D(p,R) of p) is upper-bounded by |/sub /spl delta/R///sup /spl delta//D(p,R)|((|A|+2/spl xi/+4 log n)/2n)+/spl sigma/(logn/n) where /sub /spl delta/R///sup /spl delta//D(p,R) is the partial derivative of D(p,R) with respect to R, |A| is the cardinality of A, and /spl xi/>0 is a parameter used to control the threshold in the Gold-washing algorithm. In connection with the results of Zhang, Yang, and Wei (see ibid., vol.43, no.1, p.71-91, 1997) on the redundancy of lossy source coding, this shows that the Gold-washing algorithm has the optimal convergence rate among all adaptive finite-state vector quantizers.