In this paper, a new Haar wavelet-based approach to the detection and localization of defects in grey-level texture images is presented. This new approach explores space localization properties of the discrete Haar wavelet transform (HT) and generates statistically-based parameterized texture defect detection criteria. The criteria provide the user with a possibility to control the percentage o...

The aim of this project is to analyze and analytical solution of different optimal control problems are difficult to obtain because they involve differential equations with single or multiple boundary conditions. In this dissertation, numerical methods using Haar Wavelet a represented to overcome this difficulty. The method reduces the differential equations into a set of line a matrix algebrai...

In this paper, we have presented the golden ratio-Haar wavelet based multimedia steganography. The key features of the proposed method are: 1. New Haar wavelet structure based on the Fibonacci sequence, and Golden Ratio. 2. Parametric transform dependency, as decryption key, on the security of the sensitive data. One of the important differences between the existing transform based data hiding ...

Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

Wavelet analysis as a p–adic harmonic analysis Abstract New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers is considered. This map (for p = 2) provides an equivalence between the constructed basis of eigenfunctions of the Vladimirov operator and the wavelet basis in L 2 (R) generated fro...

This paper is based on [CPSSZ00] which is to appear in Experimental Mathematics. The name wavelet was made up by French researchers [MAFG82, Mor83, GM84] for a particular class of functions. The existence of wavelet-like functions has been known since the beginning of the century (a notable example is what is known as the Haar wavelet today [Haa10]). However, only recently the unifying concepts...

Nonlinear diffusion filtering and wavelet shrinkage are two methods that serve the same purpose, namely discontinuity-preserving denoising. In this chapter we give a survey on relations between both paradigms when space-discrete or fully discrete versions of nonlinear diffusion filters are considered. For the case of space-discrete diffusion, we show equivalence between soft Haar wavelet shrink...

The Haar transform, which is one of the earliest transform functions proposed, was proposed in 1910 by a Hungarian mathematician Alfred Haar. It is found effective as it provides a simple approach for analysing the local aspects of a signal. Say we start with an image slice (one dimensional) of size , so we can write the image as Recursive Process of Decomposing an Image in terms of Sums and Di...