Intraframe transform coding of pictures for the case of a nonseparable covariance model is considered. Performances of the Walsh-Hadamard, discrete cosine and Karhunen-Loeve transforms are compared based on the compac...
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Intraframe transform coding of pictures for the case of a nonseparable covariance model is considered. Performances of the Walsh-Hadamard, discrete cosine and Karhunen-Loeve transforms are compared based on the compaction of signal energy in the transform components, and, the degree of decorrelation of the data. The results demonstrate that the performances of the discrete cosine and Karhunen-Loéve transforms compare closely, as is the case with a separable covariance model. The corresponding performance of the Walsh-Hadamard transform is inferior.
Most adaptive transform coding systems are based on a classification of transform blocks into classes of different statistical properties. In this contribution, a two-dimensional feature space for block classification...
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Most adaptive transform coding systems are based on a classification of transform blocks into classes of different statistical properties. In this contribution, a two-dimensional feature space for block classification is proposed which discriminates reliably between blocks that require very different processing. In combination with a block "activity" measurement, the introduced "spectral entropy" feature offers the possibility to stabilize the reconstruction quality of transform coding systems for each processed block on a high level.
The gain distortion function is defined as a performance measure for the comparison of orthonormal transforms on the basis of the rate distortion theory. It estimates the number of bits per picture element that can be...
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The gain distortion function is defined as a performance measure for the comparison of orthonormal transforms on the basis of the rate distortion theory. It estimates the number of bits per picture element that can be saved by transform coding. Gain distortion functions were computed for several transforms of the dimension 8 × 8. Die Gain-Distortion-Funktion ist als Gütekriterium zum Vergleich orthonormaler transformationen auf der Basis der Rate-Distortion-Theorie definiert. Sie gibt einen Schätzwer für die Anzahl von bits je Bildpunkt, die durch transformationskodierung eingespart werden können. Gain-Distortion-Funktionen werden für mehrere transformationen der Dimension 8 × 8 berechnet. En se basant sur la théorie du taux de fidélité, on définit la fonction gain-distorsion comme mesure de performance pour la comparaison des transformations orthonormales. Cette fonction estime le nombre de bits par point image que l'on peut économiser par codage de transformée. Les fonctions gain-distorsion ont été calculées pour plusieures transformations de dimension 8 sur 8.
This paper describes the results of theoretical studies made on performance of various kinds of intrafield two-dimensional transform codings (Hadamard, cosine, and slant) for carrier chrominance signals, by introducin...
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This paper describes the results of theoretical studies made on performance of various kinds of intrafield two-dimensional transform codings (Hadamard, cosine, and slant) for carrier chrominance signals, by introducing a new measure (transform coefficients of zero variance) for such coding performances. In addition, a comparative study of the performance of these transform codings is performed for different sampling frequencies (2f_{sc}, 3f_{sc}, 4f_{sc}) with the same transmission rate, taking into account the tradeoff between the number of bits assigned to a picture element at each sampling frequency and the autocorrelation between adjacent picture elements.
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 sho...
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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.
In a variety of applications, classification systems operate on compressed signals. This paper explores the design of optimal transform coders optimizing a joint classification/reconstruction criterion, where classifi...
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ISBN:
(纸本)0769518966
In a variety of applications, classification systems operate on compressed signals. This paper explores the design of optimal transform coders optimizing a joint classification/reconstruction criterion, where classification accuracy is measured using the Chernoff bound on probability of misclassification and reconstruction quality is measured using mean-squared error (MSE) distortion. Under a high-rate assumption, we show local optimality properties of the Karhunen-Loeve transform (KLT) for a certain class of Gaussian mixtures under a joint classification/MSE measure, and derive analytical expressions for optimal bit-allocation. This generalizes classical optimality properties of the KLT for Gaussian sources under the MSE criterion.
Federated learning (FL) enables distributed training via periodically synchronizing model updates among participants. Communication overhead becomes a dominant constraint of FL since participating clients usually suff...
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ISBN:
(纸本)9798350383515;9798350383508
Federated learning (FL) enables distributed training via periodically synchronizing model updates among participants. Communication overhead becomes a dominant constraint of FL since participating clients usually suffer from limited bandwidth. To tackle this issue, top-k based gradient compression techniques are broadly explored in FL context, manifesting powerful capabilities in reducing gradient volumes via picking significant entries. However, previous studies are primarily conducted on the raw gradients where massive spatial redundancies exist and positions of non-zero (top-k) entries vary greatly between gradients, which both impede the achievement of deeper compressions. Top-k may also degrade the performance of trained models due to biased gradient estimations. Targeting the above issues, we propose FedTC, a novel transform coding based compression framework. FedTC transforms gradients into a new domain with more compact energy distributions, which facilitates reducing spatial redundancies and biases in subsequent sparsification. Furthermore, non-zero entries across clients from different rounds become highly aligned in the transform domain, motivating us to partition the gradients into smaller entry blocks with various alignment levels to better exploit these alignments. Lastly, positions and values of non-zero entries are independently compressed in a block-wise manner with our customized designs, through which a higher compression ratio is achieved. Theoretical analysis and extensive experiments consistently demonstrate the effectiveness of our approach.
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...
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We present a novel algorithm for designing a transform codebook for adaptive transform coding a non-stationary source, where the codebook contains a set of or-thonormal transform matrices. The non-stationary source is...
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ISBN:
(纸本)9781665478939
We present a novel algorithm for designing a transform codebook for adaptive transform coding a non-stationary source, where the codebook contains a set of or-thonormal transform matrices. The non-stationary source is modeled by a block-wise (locally) stationary process so that all vectors in a given block can be coded using a single transform-matrix chosen from the codebook. The transform-matrix codebook is designed such that the mean-square error (MSE) of coding locally stationary blocks, averaged over the ensemble of blocks (AMSE) is minimized. First, a sequence of training vectors from the non-stationary source (such as blocks of pixels extracted from images) is segmented into locally stationary blocks of vectors. Our design algorithm starts with an initial codebook and iteratively updates the codebook for the training set, similar to the well-known generalized Lloyd algorithm for vector quantizer design. Each iteration consists of two steps: 1) the training set is partitioned into subsets by encoding the training set using the current transform codebook, and 2) the code-book is updated by computing a centroid transform-matrix for each subset. A major difference compared to the standard Lloyd algorithm however is the requirement to enforce an orthonormality constraint on the matrices in the codebook during the computation of centroids. This is accomplished by mapping the constrained problem in Euclidean space to an unconstrained problem on the Stiefel manifold. Gradient-descent on the Stiefel manifold is then used to compute the centroids. Essential to the implementation of manifold gradient-descent is an expression for the AMSE which is differentiable with respect to the transform matrix. Towards this end, we present two expressions whose matrix derivatives can be analytically obtained: 1) an approximate high-rate expression assuming Gaussian distributed source vectors, and 2) an exact finite-rate expression assuming Laplace distributed transform coefficients.
As digital imaging technology advances, the amount of image data we generate increases and the need for compressed images becomes apparent. Because lossy compression will yield higher compression ratios than lossless ...
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ISBN:
(纸本)0780377893
As digital imaging technology advances, the amount of image data we generate increases and the need for compressed images becomes apparent. Because lossy compression will yield higher compression ratios than lossless methods, objective assessment metrics of reconstructed image quality are needed. In medical applications, model observers, especially the channelized Hotelling observer, have been successfully used to predict human observer performance and to evaluate image quality for detection tasks on various backgrounds. To use model observers, however, requires knowledge of noise statistics. This paper finds closed-form expressions for the noise induced by transform coding, one of the most commonly used methods for image compression. Knowledge of the noise enables us to study the effect of image compression on the clinical utility of medical images that have been reconstructed after being compressed using transform coding. In this paper, by analyzing image compression procedures, we propose a block-based transform coding representation in 1-D form, identify the quantization noise as the sole distortion source in transform coding, and derive the compression noise statistics. We show that the probability density function (pdf) of the compression noise is defined as a function of the transform matrix and its corresponding quantization matrix in the transform coding algorithm. We prove that the compression noise is a normal distribution when the dimension of the transform (the block size) is typical. We also provide the pdf of JPEG compression noise as a function of the quantization table and the DCT transform bases. This work provides the theoretical foundation for using the model observers in closed mathematical form, and can be applied to other image compression application areas that require the statistics of compression noise as well.
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