In this paper, we study a family of analytical probability models for images within the spectral representation framework. First the input image is decomposed using a bank of filters, and probability models are imposed on the filter outputs (or spectral components). A two-parameter analytical form, called a Bessel K form, derived based on a generator model, is used to model the marginal probabi...

Non-diffracting Bessel beams, including zero-order and high-order Bessel Beams which carry orbital angular momentum (OAM), enable a variety of important applications in optical micromanipulation, sub-diffraction imaging, high speed photonics/quantum communication, etc. The commonly used ways to create Bessel beams, including an axicon or a digital hologram written to a spatial light modulator (...

It is shown that the tail probability of a Bessel process is the distributio function of a random time which is related to first and last passage times of Bessel processes. AMS Classification 60 J 25, 60 J 60, 60 E 15, 60 G 44, 60 H 10.

Delest, M. In this paper, we show that the generating function for skew Ferrers diagrams according to their width and area is the quotient of new basic Bessel functions. Nous montrons dans cet article que la fonction g&ntratrice des diagrammes de Ferrers gauches selon les paramktres ptrimttre et aire s'exprime en fonction du quotient des q analogues de deux fonctions de Bessel.

e review a recent result in modeling lower order (univariate and bivariate) probability densities of pixel values resulting from bandpass filtering of images. Assuming an object-based model for images, a parametric family of probabilities, called Bessel K forms, has been derived [1]. This parametric family matches well with the observed histograms for a large variety of images (video, range, in...

In a previous study, we discussed the expansion of two-parameter functions in a double series of Chebyshev polynomials, and, in particular, we presented coefficients for the evaluation of the modified Bessel function (2z I iifne'K,(z) to 20 decimals for all z ^ 5 and all v, 0 g v g 1. In the present study, we give similar coefficients for the evaluation of ge~'z-»l,(z) to at least 20 decimals w...

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly us...

We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman–Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler–Heine formula, that is an approximation of the Heckman–Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This ...

By considering a particular probabilistic scenario associated with coincidences, we are led to a family of functions akin to the modified Bessel function of the first kind. These are in turn solutions to a certain family of linear differential equations possessing structural similarities to the modified Bessel differential equation. The Stirling number triangle of the second kind arises quite n...

Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bes...