Image processing and analysis based on the continuous or discrete image transforms are classic techniques. The image transforms are widely used in image filtering, data description, etc. Nowadays the wavelet theorems make up very popular methods of image processing, denoising and compression. Considering that the Haar functions are the simplest wavelets, these forms are used in many methods of ...

The classical Haar construction of Brownian motion uses a binary tree of triangular wedge-shaped functions. This basis has compactness properties which make it especially suited for certain classes of numerical algorithms. We present a similar basis for the Ornstein-Uhlenbeck process, in which the basis elements approach asymptotically the Haar functions as the index increases, and preserve the...

Stream cipher systems are considered desirable and secure if composed of Boolean functions (B.Fs) that are characterized by high resiliency. Resiliency is one of the main cryptographic security criteria for a given Boolean function. One of the classes of functions satisfying high resiliency with desirable cryptographic properties include the Plateaued functions whose design construction is of s...

In this paper we characterise, in terms of the upper Dini derivative, when the Clarke subdiierential mapping of a real-valued locally Lipschitz function is a minimal weak cusco. We then use this characterisation to deduce some new results concerning Lips-chitz functions with minimal subdiierential mappings. In the papers 7] and 1], the authors investigate a class of locally Lipschitz functions ...

Wavelets are mathematical tools for hierarchically decomposing functions. Wavelet Transform has been proved to be a very useful tool for image processing in recent years. It allows a function which may be described in terms of a coarse overall shape, plus details that range from broad to narrow. The most distinctive feature of Haar Transform lies in the fact that it lends itself easily to simpl...

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the locality of their decomposition and reconstruction filters. However, Haar wavelets are not satisfactory for some applications due to their non-continuous behaviour. Having a particular level of smoothness is important for many applications. B-spline wavelets are capable of being applied t...