Clyde Hardin - Academia.edu (original) (raw)

Papers by Clyde Hardin

For p G (0, oo) and not an even integer it is proved that every isometric multiplier on an invari... more For p G (0, oo) and not an even integer it is proved that every isometric multiplier on an invariant subspace of L P (G) is a translation operator.

6c. ADDRESS (City. State and ZIP Code) 7b. ADDRESS (City. State and ZIP Coaql Statistics Dept., 3... more 6c. ADDRESS (City. State and ZIP Code) 7b. ADDRESS (City. State and ZIP Coaql Statistics Dept., 321 PH 039A, UNC AFOSR/NM *Chapel Hill, NC 27514 Bldg 410 Ba. NME O FUNING/PONSRINGBoiling APEDO 20332-6449 S& NMF F rUOIN/SPOSORNGBb. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (if appiicable) 8c. ADDRESS IXity. State and ZIP Code) 10. SOURCE OF FUNDING NOS.

Sixth Multidimensional Signal Processing Workshop

Arithmetic coding is applied to provide lossless and loss-inducing compression of optical, infrar... more Arithmetic coding is applied to provide lossless and loss-inducing compression of optical, infrared, and synthetic aperture radar imagery of natural scenes. Arithmetic coding algorithms successfully exploit the dependence structure of images through the adaptive estimation of probability distributions conditioned on pixel contexts. Several different contexts are considered, including both predictive and non-predictive variations, with both image-dependent and image-independent variations. In lossless coding experiments, arithmetic coding algorithms are shown to outperform comparable variants of both Huffman and Lempel-Ziv-Welch coding algorithms by approximately 0.5 bits per pixel. For image-dependent contexts constructed from high-order autoregressive predictors, arithmetic coding algorithms provide compression ratios as high as 4. Contexts constructed from lower-order auteregressive predictors provide compression ratios nearly as great as those of the higher-order predictors with favorable computational trades. Compression performance variations are shown to reflect the inherent sensor-dependent differences in the stochastic structure of the imagery. Arithmetic coding is also demonstrated to be a valuable addition to loss-inducing compression techniques. Code sequences derived from a lapped orthogonal transform-based vector quantization scheme are shown to be losslessly compressible using the arithmetic coding scheme. For imagery compressed to 0.5 bits per pixel, the addition of an arithmetic coder with Markov-dependent context results in additional compression ratio gains as high as 2 with no additional loss in fidelity. 'Rome Air Development Center sponsored this work under contract number F30602-87-(3-0225.

I& REPORT SECURITY CLASSIFICATION 1b. RESTRICTIVE MARKINGS * Nonclassified * 2&. SECURITY CLASSIF... more I& REPORT SECURITY CLASSIFICATION 1b. RESTRICTIVE MARKINGS * Nonclassified * 2&. SECURITY CLASSIFICATION AUTH4ORITY 3. DISTRIBUTION/AVAISTUUINSTTMN 31 a CLASSIFICATiON'DowNaRADING SCHEDULE eI=vb r101 A. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGA REPniuORT NUalimit3

Proceedings of the American Mathematical Society, 1985

There exists an Revalued mean-zero Gaussian process, all of whose projections agree with the proj... more There exists an Revalued mean-zero Gaussian process, all of whose projections agree with the projections of standard Brownian motion, yet which is not standard Brownian motion.

Probability Theory and Related Fields, 1988

For symmetric stable sequences, notions of innovation and Wold decomposition are introduced, char... more For symmetric stable sequences, notions of innovation and Wold decomposition are introduced, characterized, and their ramifications in prediction theory are discussed. As the usual covariance orthogonality is inapplicable, the non-symmetric James orthogonality is used. This leads to right and left innovations and Wold decompositions, which are related to regression prediction and least pth moment prediction, respectively. Independent innovations and Wold decompositions are also characterized; and several examples illustrating the various decompositions are presented.

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1982

A stochastic process X = {Xt: t ~ T} is called spherically generated if for each random vector X=... more A stochastic process X = {Xt: t ~ T} is called spherically generated if for each random vector X=(Xtl,...,X,n), there exist a random vector Y=(Y1,-, Ym) with a spherical (radially symmetric) distribution and a matrix A such that X is distributed as AY. X is said to have the linear regression property if ~(XoIX 1 .... ,X,) is a linear function of X1,...,X. whenever the Xj's are elements of the linear span of X. It is shown that providing the linear span of X has dimension larger than two, then X has the linear regression property if and only if it is spherically generated. The class of symmetric stable processes which are spherically generated is shown to coincide with the class of socalled sub-Gaussian processes, characterizing those stable processes having the linear regression property.

Stable Processes and Related Topics, 1991

A previous paper by the authors gives explicit formulas for the regression function of one stable... more A previous paper by the authors gives explicit formulas for the regression function of one stable random variable upon another. Although the regression may sometimes be linear, it is in general not a linear function. It involves the quotient of two integrals which cannot be computed analytically and must therefore be approximated numerically. Although the general problem of computing the integrals is straightforward in principle, the specific task is fraught with difficulties. In order to allow the practioner to apply the formulas, this paper presents a self-contained exposition of the regression problem and a software package, written in the C language, which overcomes the numerical difficulties and allows the user control over the accuracy of the approximation. The package also allows the user to compute numerically the probability density function of a stable random variable.

Stochastic Processes and their Applications, 1987

We derive spectral necessary and sufficient conditions for stationary symmetric stable processes ... more We derive spectral necessary and sufficient conditions for stationary symmetric stable processes to be metrically transitive and mixing. We then consider some important classes of stationary stable processes: Sub-Gaussian stationary processes and stationary stable processes with a harmonic spectral representation are never metrically transitive, the latter in sharp contrast with the Gaussian case. Stable processes with a harmonic spectral representation satisfy a strong law of large numbers even though they are not generally stationary. For doubly stationary stable processes. sulTicient conditions are derived for metric transitivity and mixing, and necessary and sut?icient conditions for ;I strong law of large numbers. AhfS IYYO Strhjec, Cltrssi/icorirm: Primary 6OEO7. 60GlO. 47DI0, 28c)IO stable processes * ergodic theory * stationary processes l spectral representations Research supported by the Air Force Ollke of Scientific Research Contract No. AFOSR F49620 82 c 0009.

Journal of Multivariate Analysis, 1982

The so-called spectral representation theorem for stable processes linearly imbeds each symmetric... more The so-called spectral representation theorem for stable processes linearly imbeds each symmetric stable process of index p into Lp (0 < p < 2). We use the theory of Lp isometries for 0 < p < 2 to study the uniqueness of this representation for the non-Gaussian stable processes. We also determine the form of this representation for stationary processes and for substable processes. Complex stable processes are defined, and a complex version of the spectral representation theorem is proved. As a corollary to the complex theory we exhibit an imbedding of complex L' into real or complex Lp for 0 < p < q < 2.

The Annals of Applied Probability, 1991

Pacific Journal of Mathematics, 1983