Allen R. Miller

Intensity and phase statistics of multilook polarimetric and interferometric SAR imagery

Polarimetric and interferometric SAR data are frequently multilook processed for speckle reduction and data compression. The statistical characteristics of multilook data are quite different from those of single-look data. The authors investigate the statistics of their intensity and phase. Probability density function (PDFs) of the multilook phase difference, magnitude of complex product, and intensity and amplitude ratios between two components of the scattering matrix are derived, and expressed in closed forms. The PDFs depend on the complex correlation coefficient and the number of looks. Comparisons of these theoretically derived PDFs are made to measurements from NASA/JPL AIRSAR data. The results of this paper can be applied to feature classification using polarimetric SAR and to the estimation of decorrelation effects of the interferometric SAR. >

Covert channels and anonymizing networks

There have long been threads of investigation into covert channels, and threads of investigation into anonymity, but these two closely related areas of information hiding have not been directly associated. This paper represents an initial inquiry into the relationship between covert channel capacity and anonymity, and poses more questions than it answers. Even this preliminary work has proven difficult, but in this investigation lies the hope of a deeper understanding of the nature of both areas. MIXes have been used for anonymity, where the concern is shielding the identity of the sender or the receiver of a message, or both. In contrast to traffic analysis prevention methods which conceal larger traffic patterns, we are concerned with how much information a sender to a MIX can leak to an eavesdropping outsider, despite the concealment efforts of MIXes acting as firewalls.

Simple timing channels

We discuss the different ways of defining channel capacity for certain types of illicit communication channels. We also correct some errors from the literature, offer new proofs of some historical results, and give bounds for channel capacity. Special function techniques are employed to express the results in closed form. We are interested in a specific type of covert channel, a timing channel. A timing channel exists if it is possible for High to interfere with the system response time to an input by Low. Therefore, a timing channel is a communication channel where the output alphabet is constructed from different time values. However, the thrust of the paper is the analysis of timing channels that are discrete, memoryless, and noiseless. We call such a timing channel a simple timing channel (STC).<<ETX>>

Statistics of phase difference and product magnitude of multi-look processed Gaussian signals

The phase difference and the product of two complex Gaussian signals are important parameters in the study of interferometry and polarimetry. To reduce statistical variations, polarimetric and inte...

Reduction of a class of Fox-Wright Psi functions for certain rational parameters

Abstract The Fox-Wright Psi function is a special case of Foxs H -function and a generalization of the generalized hypergeometric function. In the present paper, we show that the Psi function reduces to a single generalized hypergeometric function when certain of its parameters are integers and to a finite sum of generalized hypergeometric functions when these parameters are rational numbers. Applications to the solution of algebraic trinomial equations and to a problem in information theory are provided. A connection with Meijers G -function is also discussed.

Karlsson–Minton summation theorems for the generalized hypergeometric series of unit argument

We give easy derivations of the Karlsson–Minton summation formulas for the generalized hypergeometric series of unit argument by employing elementary combinatorial identities for binomial coefficients and Stirling numbers of the second kind. In addition, we record new generalizations of these summation formulas.

Transformation formulas for the generalized hypergeometric function with integral parameter differences

Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions r+2Fr+1(x) and r+1Fr+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers. Certain quadratic transformations for the former function, as well as a summation theorem when x = 1, are also considered. Mathematics Subject Classification: 33C15, 33C20

On the Mellin transform of products of Bessel and generalized hypergeometric functions

We deduce in an elementary way representations for the Mellin transform of a product of Bessel functions 0F1[−a2x2] and generalized hypergeometric functions pFp+1[−b2x2] for a,b>0. As a corollary we obtain a transformation formula for p+1Fp[1] which was discovered by Wimp in 1987 by using Baileys method for the specialization 3F2[1].

Remarks on a generalized beta function

Abstract We show that a certain generalized beta function B(x,y;b) which reduces to Eulers beta functions B(x,y) when its variable b vanishes and preserves symmetry in its parameters may be represented in terms of a finite number of well known higher transcendental functions except (possibly) in the case when one of its parameters is an integer and the other is not. In the latter case B(x,y;b) may be represented as an infinite series of either Wittaker functions or Laguerre polynomials. As a byproduct of this investigation we deduce representations for several infinite series containing Wittaker functions, Laguerre polynomials, and products of both.

A summation formula for Clausen's series 3F2(1) with an application to Goursat's function 2F2(x)

A new summation formula for Clausens series 3F2(1) is derived in two different ways and used to obtain a reduction formula for the Kampe de Feriet function Fp:2;0q:2;0 [− x, x]. The specialization p = q = 0 of the latter result reduces to a Kummer-type transformation formula for the generalized hypergeometric function 2F2(x) which has recently been deduced by R B Paris who employed other methods.