Digital image coding using legendre transform

Image coding can be implemented through DPCM, transform, hybrid, or segmentation coding techniques. Some transform coding techniques, such as cosine and Hadamard, have been exhaustively analyzed and evaluated, while others, such as Legendre, have not. This paper introduces the use of Legendre transform in image coding. The transform matrix for different block sizes is calculated, the fast algorithm is derived, and the performance is evaluated through both mean square error and subjective quality. The results obtained have indicated that the system performance is comparable with that of optimum KLT and cosine transforms; moreover, it is simpler in implementation.     

Coding isotropic images

Rate-distortion functions for 2-dimensional homogeneous isotropic images are compared with the performance of five source encoders designed for such images. Both unweighted and frequency weighted mean-square error distortion measures are considered. The coders considered are a) differential pulse code modulation (DPCM) using six previous samples or picture elements (pels) in the prediction--herein called 6-pel DPCM, b) simple DPCM using single-sample prediction, c) 6-pel DPCM followed by entropy coding, d)8 times 8discrete cosine transform coding, and e)4 times 4Hadamard transform coding. Other transform coders were studied and found to have about the same performance as the two transform coders above. With the mean-square error distortion measure, 6-pel DPCM with entropy coding performed best. Next best was the8 times 8discrete cosine transform coder and the 6-pel DPCM--these two had approximately the same distortion. Next were the4 times 4Hadamard and simple DPCM, in that order. The relative performance of the coders changed slightly when the distortion measure was frequency weighted mean-square error. FromR = 1to 3 bits/pel, which was the range studied here, the performances of all the coders were separated by only about 4 dB.     

The Effectiveness and Efficiency of Hybrid Transform/DPCM Interframe Image Coding

We seek to evaluate the efficiency of hybrid transform/ DPCM interframe image coding relative to an optimal scheme that minimizes the mean-squared error in encoding a stationary Gaussian image sequence. The stationary assumption leads us to use the asymptotically optimal discrete Fourier transform (DFT) on the full frame of an image. We encode an actual image sequence with full-frame DFT/DPCM at several rates and compare it to previous interframe coding results with the same sequence. We also encode a single frame at these same rates using a full-frame DFT to demonstrate the inherent coding gains of interframe transform DPCM over intraframe coding. We then generate a pseudorandom image sequence with precise Gauss-Markov statistics and encode it by hybrid full-frame DFT/DPCM at various rates. We compare the signal-to-noise ratios (SNR's) of these reconstructions to the optimal ones calculated from the rate-distortion function. We conclude that in a medium rate range below 1 bit/pel/frame where reconstructions for hybrid transform/ DPCM may be unsatisfactory, there is enough margin for improvement to consider more sophisticated coding schemes.     

Hybrid Coding of Pictorial Data

Two hybrid coding systems utilizing a cascade of a unitary transformation and differential pulse code modulators (DPCM) systems are proposed. Both systems encode the transformed data by a bank of DPCM systems. The first system uses a one-dimensional transform of the data where the second one employs two-dimensional transformations. Theoretical results for Markov data and experimental results for a typical picture are presented for Hadamard, Fourier, cosine, slant, and the KarhunenLoeve transformations. The visual effects of channel error and also the impact of noisy channel on the performance of the hybrid system, measured in terms of the signal-to-noise ratio of the encoder, is examined and the performance of this system is compared to the performances of the two-dimensional DPCM and the standard two-dimensional transform encoders.     

DCT/DPCM Processing of NTSC Composite Video Signal

This paper describes two different schemes of DCT/ DPCM processing of digital NTSC composite video signal. The first scheme (line processing) is based on applying the discrete cosine transform (DCT) along each horizontal line and then implementing the differential pulse code modulation (DPCM) in the vertical direction on the semitransformed image. The second scheme (block processing) involves DCT of (4 × 4) subblocks followed by adaptive DPCM to reduce intersubblock correlation. Based on the statistics of the prediction error, variable bit quantizers optimized for minimizing the mean-square quantization error are developed. These techniques lead to reduced bit rates for transmitting the color video at broadcast standards. Both original and processed color images in composite form are displayed for subjective evaluation. The effects of channel error on block processing are also investigated.     

基于二维APDCSF的列率子带特征编码方法

提出了一种子带编码的新方法。该方法利用二维全相位离散反余弦列率滤波器（APDCSF）对图像进行子带分解;对于低频子带图像采用直接斜交多重亚采样和基于全相位离散反余弦列牢滤波器（APDICsF）的多重旋转内插恢复．而对高频子带图像利用直方图自动阈值化提取如边缘和线等特征的图像元;根据各个子带的图像元的特征分别进行编码压缩,解压缩后利用凸集投影重建原始图像。该方法消除了传统的离散余弦变换（DCT）编码的方块化效应,与基于小波变换的子带特征编码方法相比,计算复杂度小,压缩率高,主观视觉性能好,对于灰阶图像可达到0．1～0．3bpp,特别适用于低比特率图像压缩。     

Multilayer subband-based video coding

A motion compensated interframe subband coding algorithm suitable for a wide range of video coding applications is described. In this approach the spectrum of each frame of video signal is first decomposed into smaller frequency bands where each can then be coded accordingly. For the best performance a combination of hybrid DCT/DPCM (discrete cosine transform/differential pulse code modulation), interframe DPCM, and intraframe PCM was considered. To preserve its hierarchical structure each band is coded independently of higher frequency bands but can share information with the lower bands. A simulation was carried out for HDTV sequences     

DCT transform coding of stereo images for multimedia applications

One form of multimedia finding increasing utility in factory automation is stereo imaging. Its uses include remote operation, telepresence, and object positioning. Stereo imaging, with doubled frames, requires high data-rate collection and transmission. Image compression techniques can be utilized to reduce the transmission bandwidth and/or storage space requirements of the stereo pair. This paper develops image compression techniques specific to stereo imaging and compares the performance with nonstereo methods. Disparity compensated residual image coding exploits the redundancy between the two images in a stereo pair. Stereo residuals possess special features that can be exploited within a discrete cosine transform (DCT) image coding framework. Use of these features results in several decibels of performance enhancement across a range of scene types. This approach provides its best performance below 0.75 b/pixel bitrate for 8-b grayscale imagery and below 2 b/pixel for 24-b color imagery     

Image data compression: A review

With the continuing growth of modern communications technology, demand for image transmission and storage is increasing rapidly. Advances in computer technology for mass storage and digital processing have paved the way for implementing advanced data compression techniques to improve the efficiency of transmission and storage of images. In this paper a large variety of algorithms for image data compression are considered. Starting with simple techniques of sampling and pulse code modulation (PCM), state of the art algorithms for two-dimensional data transmission are reviewed. Topics covered include differential PCM (DPCM) and predictive coding, transform coding, hybrid coding, interframe coding, adaptive techniques, and applications. Effects of channel errors and other miscellaneous related topics are also considered. While most of the examples and image models have been specialized for visual images, the techniques discussed here could be easily adapted more generally for multidimensional data compression. Our emphasis here is on fundamentals of the various techniques. A comprehensive bibliography with comments is included for a reader interested in further details of the theoretical and experimental results discussed here.     

A codec for HDTV signal transmission through terrestrial and satellite digital links

A codec for digital transmission of HDTV is described. The bit-rate compression algorithm is based on advanced techniques such as spatial discrete cosine transform (DCT), temporal differential PCM (DPCM), variable length coding. The codec is designed to operate with both the interlaced studio systems 1125/60 and 1250/50, and, thanks to the inherent flexibility of the packet structure, a wide range of line bit-rates can be used as a compromise between video quality and bit-rate constraints of the digital transmission link. The flexibility of the HDTV codec is highlightened through examples of applications over satellite digital links in practical situations.     

HDTV communication systems in broadband communication networks

Two high-definition television (HDTV) communication systems created for broadband communication networks are discussed. Nationwide HDTV transmission and distribution services and HDTV subscriber distribution services are examined. A network architecture for high-quality HDTV transmission is described. The transmission bit rates of HDTV services, which are the basic factors in constructing the network frame, are considered. Two HDTV coding algorithms, subband discrete cosine transform (DCT) and subband differential pulse-code modulation (DPCM) are described, and their coding bit rates discussed. A synchronous-digital-hierarchy-based synchronous transfer mode network design suitable for the transmission of HDTV signals in broadband communication networks are described     

Transform and Hybrid Transform/DPCM Coding of Images Using Pyramid Vector Quantization

The transform and hybrid transform/DPCM methods of image coding are generalized to allow pyramid vector quantization of the transform coefficients. An asymptotic mean-squared error performance expression is derived for the pyramid vector quantizer and used to determine the optimum rate assignment for encoding the various transform coefficients. Coding simulations for two images at average rates of 0.5-1 bit/pixel demonstrate a 1-3 dB improvement in signal-to-noise ratio for the vector quantization approach in the hybrid coding, with more modest improvements in signal-to-noise ratio in the transform coding. However, this improvement is quite noticeable in image quality, particularly in reducing "blockiness" in the low bit rate encoded images.     

Compression of hyperspectral imagery using the 3-D DCT and hybridDPCM/DCT

Two systems are presented for compression of hyperspectral imagery which utilize trellis coded quantization (TCQ). Specifically, the first system uses TCQ to encode transform coefficients resulting from the application of an 8×8×8 discrete cosine transform (DCT). The second systems uses DPCM to spectrally decorrelate the data, while a 2D DCT coding scheme is used for spatial decorrelation. Side information and rate allocation strategies are discussed. Entropy-constrained code-books are designed using a modified version of the generalized Lloyd algorithm. These entropy constrained systems achieve compression ratios of greater than 70:1 with average PSNRs of the coded hyperspectral sequences exceeding 40.0 dB     

Theoretical Comparison Between DPCM and Transform Coding Regarding the Robustness of Coding Performance for Variation of Picture Statistics

Since DPCM and transform coding are two fundamental approaches to high-efficiency (bit reduction) coding, it is important to clarify the basic coding characteristics of these approaches and the differences between them in order to utilize the high-efficiency coding method effectively. It is important to compare them not only from the standpoint of coding performance as optimized coding schemes based on the statistics of the input picture signal, but also from that of the robustness of coding performance for the variation of picture statistics to be coded. This paper theoretically compares the robustness of the coding performance of DPCM having a two-dimensional predictor with that of a two-dimensional Hadamard transform coding in an intrafield coding method of the NTSC composite signal. The comparison provides theoretical evidence that transform coding is more stable than DPCM, and this tendency is marked at lower bit rates such as 1 or 2 bits/pel, while DPCM has a higher coding performance for pictures with high autocorrelation.     

Shape-VQ-based lossless hybrid ADPCM/DCT coder

The discrete cosine transform (DCT) has been shown as an optimum encoder for sharp edges in an image (Andrew and Ogunbona, 1997). A conventional lossless coder employing differential pulse code modulation (DPCM) suffers from significant deficiencies in regions of discontinuity, because the simple model cannot capture the edge information. This problem can be partially solved by partitioning the image into blocks that are supposedly statistically stationary. A hybrid lossless adaptive DPCM (ADPCM)/DCT coder is presented, in which the edge blocks are encoded with DCT, and ADPCM is used for the non-edge blocks. The proposed scheme divides each input image into small blocks and classifies them, using shape vector quantisation (VQ), as either edge or smooth. The edge blocks are further vector quantised, and the side information of the coefficient matrix is saved through the shape-VQ index. Evaluation of the compression performance of the proposed method reveals its superiority over other lossless coders     

3D scanning-based compression technique for digital hologram video

In this paper, we proposed an efficient coding method for digital hologram video using a three-dimensional (3D) scanning method and two-dimensional (2D) video compression technique. It consists of separation of the captured 3D image into R, G, and B color space components, localization by segmenting the fringe pattern in to M×N [pixel²], frequency-transform by 2D discrete cosine transform (2D DCT), 3D-scanning the segments to form a video sequence, classification of coefficients, and hybrid video coding with H.264/AVC, differential pulse code modulation (DPCM), and lossless coding method. The experimental results with this method showed that the proposed method has compression ratios of 8–16 times higher than the previous researches. Thus, we expect it to contribute to reduce the amount of digital hologram data for communication or storage.     

Comparison Between DPCM and Hadamard Transform Coding in the Composite Coding of the NTSC Color TV Signal

Since differential-pulse-code modulation (DPCM) and orthogonal transform coding (OTC) are the most fundamental methods of high-efficiency coding (bit-reduction method), it is important to clarify the basic coding characteristics of these methods and the difference between them in order to utilize the bit-reduction method effectively. This paper theoretically as well as experimentally compares the coding efficiency of a DPCM having a two-dimensional predictor with that of a two-dimensional Hadamard transform coding method (HTC) in the intrafield coding of the NTSC composite signal. The comparison evidenced that the distinctive difference in coding characteristics between DPCM and HTC depends greatly on the power level of carrier chrominance signals. That is, it is confirmed theoretically and experimentally that the coding efficiency of the HTC is far lower than that of the DPCM in the case of a signal having a high power level carrier chrominance signal such as a color-bar signal.     

A Unified Representation of Differential Pulse-Code Modulation (DPCM) and Transform Coding Systems

We consider a transform coding system that uses a lower-triangular transformation to uncorrelate the data. Based on this transformation we propose a generalized differential pulse code modulation (DPCM) system and show that at high bit rates it performs almost as well as coding by the method of principal components (Karhunen-Loeve transformation). This study connects the transform coding system to the DPCM encoder by showing that the proposed system simplifies to a standard DPCM encoder for Markov data.     

Noncausal predictive image codec

The paper describes a lossy image codec that uses a noncausal (or bilateral) prediction model coupled with vector quantization. The noncausal prediction model is an alternative to the causal (or unilateral) model that is commonly used in differential pulse code modulation (DPCM) and other codecs with a predictive component. We show how to obtain a recursive implementation of the noncausal image model without compromising its optimality and how to apply this in coding in much the same way as a causal predictor. We report experimental compression results that demonstrate the superiority of using a noncausal model based predictor over using traditional causal predictors. The codec is shown to produce high-quality compressed images at low bit rates such as 0.375 b/pixel. This quality is contrasted with the degraded images that are produced at the same bit rates by codecs using causal predictors or standard discrete cosine transform/Joint Photographic Experts Group-based (DCT/JPEG-based) algorithms.     

Optical computing techniques for image/video compression

The advantage of optics is its capability of providing highly parallel operations in a three-dimensional space. In this paper, we propose optical architectures to execute various image compression techniques. We optically implement the following compression techniques: transform coding, vector quantization, video coding. We show many generally used transform coding methods, for example, the cosine transform, can be implemented by a simple optical system. The transform coding can be carried out in constant time. Most of this paper is concerned with an innovative optical system for vector quantization using holographic associative matching. Limitations of conventional vector quantization schemes are caused by a large number of sequential searches through a large vector space. Holographic associative matching provided by multiple exposure holograms can offer advantageous techniques for vector-quantization-based compression schemes. Photorefractive crystals, which provide high-density recording in real time, are used as our holographic media. The reconstruction alphabet can be dynamically constructed through training or stored in the photorefractive crystal in advance. Encoding a new vector can be carried out by holographic associative matching in constant time. An extension to interframe coding using optical block matching methods is also discussed