Journal ArticleDOI
Further decomposition of the Karhunen-Loève series representation of a stationary random process
TLDR
It is shown how the Karhunen-Loeve (K-L) series representation for a finite sample of a discrete random sequence, stationary to the second order, may be further decomposed into a pair of series by utilizing certain symmetry properties of the covariance matrix of the sequence.Abstract:
It is shown how the Karhunen-Loeve (K-L) series representation for a finite sample of a discrete random sequence, stationary to the second order, may be further decomposed into a pair of series by utilizing certain symmetry properties of the covariance matrix of the sequence. The theory is applied to the particular example of a first-order Markov sequence, the series representation of which has not so far been reported in the literature. The generalization to the case of continuous random functions on a finite interval is similar and is therefore only briefly described.read more
Citations
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Journal ArticleDOI
Image data compression: A review
TL;DR: A large variety of algorithms for image data compression are considered, starting with simple techniques of sampling and pulse code modulation (PCM) and state of the art algorithms for two-dimensional data transmission are reviewed.
Proceedings Article
Local Decorrelation For Improved Pedestrian Detection
TL;DR: Inspired by recent work on discriminative decorrelation of HOG features, an efficient feature transform that removes correlations in local neighborhoods is proposed, resulting in an overcomplete but locally decorrelated representation ideally suited for use with orthogonal decision trees.
Journal ArticleDOI
Theoretical foundations of transform coding
TL;DR: Discusses various aspects of transform coding, including: source coding, constrainedsource coding, the standard theoretical model fortransform coding, entropy codes, Huffman codes, quantizers, uniform quantization, bit allocation, optimal transforms, transforms visualization, partition cell shapes, autoregressive sources and departures form the standard model.
Journal ArticleDOI
A Sinusoidal Family of Unitary Transforms
TL;DR: A new family of unitary transforms is introduced and it is shown that the well-known discrete Fourier, cosine, sine, and the Karhunen-Loeve (KL) (for first-order stationary Markov processes) transforms are members of this family.
Journal ArticleDOI
Relation between the Karhunen Loève and cosine transforms
TL;DR: The cosine transform is demonstrated theoretically by showing that it can be derived from the optimum (Karhunen-Loeve) transform in the limiting case when the adjacent data-element correlation tends to unity.
References
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Stochastic processes and statistical inference
TL;DR: In this article, the possibility of applying statistical concepts and methods of inference to stochastic processes, and obtaining practically working methods of this kind by studying special cases of inference is discussed.
Journal ArticleDOI
An Approach to Time Series Analysis
TL;DR: In this paper, a new approach to regression problems using reproducing kernel Hilbert spaces is described, and the authors show the close relation between statistical communication and control theory, probabilistic (and Hilbert space) theory of stochastic processes processing finite second moments, and statistical theory of regression analysis, correlation analysis, and spectral analysis of time series.
On Linear Methods in Probability Theory
K. Karhunen,Ivan Selin +1 more
TL;DR: In this paper, a summary of the most important properties of infinite sets of random variables, following Kolmogorov, is presented. Butler et al. construct the Hilbert space corresponding to a given set of random variable with finite dispersions, discuss random functions and their simplest correlation properties, present a new definition of the integral of a random function, defines the spectral representation, and considers applications of stationary random functions.