This paper presents a wavelet-based watermarking method for copyright protection of still images. Watermarks are structured in such a way to attain spatial self-similarity with respect to a cartesian grid. Embedding and detection are performed in the wavelet domain allowing thus multiresolution detection. The novelty of the current approach is the use of self-similar watermarks (quasi scaleinva...

In this work we review the parameterization of filter coefficients of compactly supported orthogonal wavelets used to implement the discrete wavelet transform. We also present the design of wavelet based filters as a constrained optimization problem where a genetic algorithm can be used to improve the compression ratio on gray scale images by minimizing their entropy and we develop a quasi-perf...

Empirical mode decomposition (EMD) and Empirical wavelet transform (EWT) are recently developed adaptive signal processing tools. These techniques decompose a signal accordingly to its contained information. The main issue with EMD is its lack of theory and in case of EWT a prior knowledge of the signal is required. IMF’s obtained as a result of applying EMD are quasi-orthogonal .This paper sug...

In this paper we model linear inverse problems with long-range dependence by a fractional Gaussian noise model and study function estimation based on observations from the model. By using two wavelet-vaguelette decompositions, one for the inverse problem which simultaneously quasi-diagonalizes both the operator and the prior information and one for long-range dependence which decorrelates fract...

Lecture 1. Harmonic Analysis of Measures: Analysis on Fractals Lecture 2. Spectra of measures, tilings, and wandering vectors Lecture 3. The universal tiling conjecture in dimension one and operator fractals Lecture 4. Representations of Cuntz algebras associated to quasi-stationary Markov measures Lecture 5. The Cuntz relations and kernel decompositions Lecture 6. Harmonic analysis of wavelet ...

[1] We report on simultaneous measurements of the westward propagating quasi 5-day wave in the occurrence rate of noctilucent clouds (NLCs) and the temperature field at NLC altitude during the 2005 NLC season in the northern hemisphere. NLCs are detected using SCIAMACHY/ Envisat limb scattering measurements, and the temperature profiles are measured with MLS/Aura. Quasi 5-day wave signatures ar...

Abstract: New numerical techniques are presented for the solution of a class of the variable order fractional advection-diffusion equation with a nonlinear source term on one-dimensional finite domain. Quasiwavelet and double quasi-wavelet are used for the spatial discretization. For the time stepping, Euler method is considered. We also tested the method proposed on several problems with very ...

This article considers the error of integrating multivariate Haar wavelet series by quasi-Monte Carlo rules using scrambled digital nets. Both the worst-case and random-case errors are analyzed. It is shown that scrambled net quadrature has optimal order. Moreover, there is a simple formula for the worst-case error.

The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly different spatial directions a simulation becomes computationally very expensive due to the large number degrees freedom. An example such domain are cables inside magnets particle accelerators. For translationally invariant domains, this work proposes quasi-...