A novel method for coding of images using the discrete cosine transform is presented. It is based on a modification of the idea of reducing subthreshold coefficients to zero during transform coding. A simple analysis shows that if the subthreshold coefficients are represented by reduced magnitudes other than zero, then the net error that results in a reconstructed pixel is less than if the coefficients have zero value. Based on this reasoning, the subthreshold coefficients are grouped according to their magnitudes, and only the average value of the coefficients in each group is selected in place of all the members of that group during coding. During image reconstruction, the average value of each group is used to generate all the members of that group. By selecting only one coefficient to represent many, the compression ratio is greatly improved.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

Cited by 0

Transform picture coding

P. A. Wintz · Proceedings of the IEEE · 1972

Picture coding by first dividing the picture into sub-pictures and then performing a linear transformation on each sub-picture cud quantizing and coding the resulting coefficients is introduced from a heuristic point of view. Various transformation, quantization, and coding strategies are discussed. A survey of all known applications of these techniques to monochromatic image coding is presented along with a summary of the dependence of performance on the basic system parameters and some conclusions.

Cited by 289

Nonlinear Transform Coding

Johannes Ballé, Philip A. Chou, David Minnen et al. · IEEE Journal of Selected Topics in Signal Processing · 2020

We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have superseded them in terms of rate-distortion performance under established perceptual quality metrics such as MS-SSIM. We assess the empirical rate-distortion performance of NTC with the help of simple example sources, for which the optimal performance of a vector quantizer is easier to estimate than with natural data sources. To this end, we introduce a novel variant of entropy-constrained vector quantization. We provide an analysis of various forms of stochastic optimization techniques for NTC models; review architectures of transforms based on artificial neural networks, as well as learned entropy models; and provide a direct comparison of a number of methods to parameterize the rate-distortion trade-off of nonlinear transforms, introducing a simplified one.

Cited by 3Open access

Pyramid transform coding

L. Wang, M. Goldberg · IEE Proceedings I Communications Speech and Vision · 1992

In the pyramid transform coding, the input image of size 2n × 2n is first decomposed into a set of blocks of size 2m × 2m, where m<n. Then, each block undergoes a two-dimensional discrete cosine transform 2D-DCT of size 2m × 2m. The resulting coefficients are reorganised into 2m × 2m transform subimages of size 2n-m × 2n-m each corresponding to a coefficient order. For each subimage, a transform mean subpyramid is formed by successively averaging over 2 × 2 neighbouring values. The corresponding transform difference subpyramid is then built up by taking the differences between successive levels in the transform mean subpyramid. The 2m × 2m transform difference subpyramids are concatenated and rearranged to form a transform difference pyramid. The transform difference pyramid can be used to form a transform mean pyramid, where the intermediate levels of the transform mean pyramid are simply the reduced-size approximations of the block transformed image. This implies that progressive image transmission can be achieved by transmitting the transform difference pyramid. The transform difference pyramid is shown to reduce the correlation between the neighbouring transform blocks. Therefore, more efficient transmission is obtained by transmitting the transform difference pyramid, instead of the original block DCT image and the transform mean pyramid. Before transmission, the transform difference pyramid is either scale or vector quantised and encoded starting from the top level where the residual errors introduced at each level are delivered to and reprocessed at the next level. The simulation results demonstrate that, by using vector quantisation, excellent quality is achieved at a bit rate of about 0.55 bits/ pixel. The pyramid transform coding scheme is shown to be competitive with variable-length transform coding.

Cited by 1

Region Oriented Transform Coding

C. Christopoulos · VUBIR (Vrije Universiteit Brussel) · 1993

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Generalized triangular transform coding

Ching-Chih Weng, Chun‐Yang Chen, P. P. Vaidyanathan · 2009

A general family of optimal transform coders (TC) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang, et al. This family includes the Karhunen-Loeve transform (KLT), and the prediction-based lower triangular transform (PLT) introduced by Phoong and Lin, as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to those of the KLT and the PLT. Even though the PLT is not applicable for vectors which are not blocked versions of scalar wide sense stationary (WSS) processes, the GTD based family includes members which are natural extensions of the PLT, and therefore also enjoy the so-called MINLAB structure of the PLT which has the unit noise-gain property. Other special cases of the GTD-TC are the GMD (geometric mean decomposition) and the BID (bidiagonal transform). The GMD in particular has the property that the optimal bit allocation (which is required for achieving the maximum coding gain) is a uniform allocation, thereby eliminating the need for bit allocation.

Cited by 1

The coding-optimal transform

Cynthia Archer, Todd K. Leen · 2002

We propose a new transform coding algorithm that integrates all optimization steps into a coherent and consistent framework. Each iteration of the algorithm is designed to minimize coding distortion as a function of both the transform and quantizer designs. Our algorithm is a constrained version of the Linde-Buzo-Gray (LBG) algorithm for vector quantizer design. The reproduction vectors are constrained to lie at the vertices of a rectangular grid. A significant result of our approach is a new transform basis specifically designed to minimize mean-squared quantization distortion for both fixed-rate and entropy-constrained coding. For Gaussian distributed data, this transform reduces to the Karhunen-Loeve transform (KLT). However, in general the coding-optimal transform (COT) differs from the KLT enough to provide up to 1 dB improvement in compressed signal-to-noise ratio (SNR) on images. We describe a practical algorithm that finds the COT for a given signal. In addition, we present image compression results demonstrating the SNR improvement achieved with our algorithm relative to KLT based transform coding.

Cited by 3

Transform coding of image.

CUHK Digital Repository (Chinese University of Hong Kong) · 1988

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Motion-Compensated Transform Coding

Arun N. Netravali, J.A. Stuller · Bell System Technical Journal · 1979

Interframe hybrid transform/dpcm coders encode television signals by taking a spatial transform of a block of picture elements in a frame and predictively coding the resulting coefficients using the corresponding coefficients of the spatial block at the same location in the previous frame. These coders can be made more efficient for scenes containing objects in translational motion by first estimating the translational displacement of objects and then using coefficients of a spatially displaced block in the previous frame for prediction. This paper presents simulation results for such motion-compensated transform coders using two algorithms for estimating displacements. The first algorithm, which is developed in a companion paper, recursively estimates the displacements from the previously transmitted transform coefficients, thereby eliminating the need to transmit the displacement estimates. The second algorithm, due to Limb and Murphy, estimates displacements by taking ratios of accummulated frame difference and spatial difference signals in a block. In this scheme, the displacement estimates are transmitted to the receiver. Computer simulations on two typical real-life sequences of frames show that motion-compensated coefficient prediction results in coder bit rates that are 20 to 40 percent tower than conventional interframe transform coders using “frame difference of coefficients.” Comparisons of bit rates for approximately the same picture quality show that the two methods of displacement estimation are quite similar in performance with a slight preference for the scheme with recursive displacement estimation.

Cited by 37

Basic Transform Video Coding

Barry S. Barnett · Elsevier eBooks · 2009

Cited by 1

Toward Textual Transform Coding

Tsachy Weissman · IEEE BITS the Information Theory Magazine · 2023

Inspired by recent work on compression with and for humans, the success of transform-based approaches to information processing, and the rise of powerful language-based AI, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">textual transform coding</i> . It shares some of its key properties with traditional transform-based coding underlying much of our current multimedia compression technologies. It can form the basis for compression at bit rates until recently considered uselessly low, and for boosting human satisfaction from reconstructions at more traditional bit rates.

Cited by 6

Beyond Traditional Transform Coding

Vivek K Goyal · 1998

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Slant Transform Image Coding

William K. Pratt, Wen-Hsiung Chen, L. R. Welch · IEEE Transactions on Communications · 1974

A new unitary transform called the slant transform, specifically designed for image coding, has been developed. The transformation possesses a discrete sawtoothlike basis vector which efficiently represents linear brightness variations along an image line. A fast computational algorithm has been found for the transformation. The slant transformation has been utilized in several transform image-coding systems for monochrome and color images. Computer simulation results indicate that good quality coding can be accomplished with about 1 to 2 bits/pixel for monochrome images and 2 to 3 bits/pixel for color images.

Cited by 216

On Interframe Transform Coding

T. Natarajan, N. Ahmed · IRE Transactions on Communications Systems · 1977

This paper is concerned with interframe coding of monochrome pictures using 3-dimensional transforms. First, an algorithm which enables the vector processing of 3-dimensional arrays is derived. Next, this algorithm is used in an interframe transform coding experiment. Picture data (6 bits/pel) is processed in ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4 \times 4 \times 4</tex> ) blocks using the Walsh-Hadamard transform (WHT), and the discrete cosine transform (DCT). The corresponding reconstructed pictures (1 bit/pel) are included.

Cited by 33