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...

We propose a level-crossing A/D (LCA/D) converter which can be modelled with an oversampling A/D followed by a low resolution quantizer. In this paper we will study the reconstruction of non-bandlimited inputs processed by such a system and compare its performance to uniform sampling. Index Termslevel-crossing sampling, MSE, Haar wavelets, bitrate.

Figure 1: Multiple registered image channels are computed using various transformations of the input image; next, features such as local sums, histograms, and Haar wavelets are computed efficiently using integral images. Such features, which we refer to as integral channel features, naturally integrate heterogeneous sources of information, have few parameters, and result in fast, accurate detec...

Due to the extensive use of digital media applications, multimedia security and copyright protection has gained tremendous importance. Digital Watermarking is a technology used for the copyright protection of digital applications. In this project, a comprehensive approach for watermarking digital image is introduced. We propose a hybrid digital watermarking scheme based on Discrete Wavelet Tran...

This article defines and studies a new class of non-stationary random processes constructed from discrete non-decimated wavelets which generalizes the Cramér (Fourier) representation of stationary time series. We define an evolutionary wavelet spectrum (EWS) which quantifies how process power varies locally over time and scale. We show how the EWS may be rigorously estimated by a smoothed wavel...

Images require substantial storage and transmission resources, thus image compression is advantageous to reduce these requirements. The objective of this paper is to evaluate a set of wavelets for image compression. Image compression using wavelet transforms results in an improved compression ratio. Wavelet transformation is the technique that provides both spatial and frequency domain informat...

In this study, we analyze the performance of a numerical scheme based on 3-scale Haar wavelets for dynamic Euler-Bernoulli equation, which is fourth order time dependent partial differential equation. This type equations governs behaviour vibrating beam and have many applications in elasticity. For its solution, first rewrite equation as system by introducing new variable, then use finite diffe...

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group suq(2) in one limit, and approaches a Fourier series generating alge...

Abstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

Several studies have demonstrated the effectiveness of Haar wavelets in reducing large amounts of data down to compact wavelet synopses that can be used to obtain fast, accurate approximate query answers. While Haar wavelets were originally designed for minimizing the overall root-mean-squared (i.e., L2-norm) error in the data approximation, the recently-proposed idea of probabilistic wavelet s...