Wavelet packet decompositions generalize the classical pyramidal wavelet structure. We use the vast amount of possible wavelet packet decomposition structures to create a secret wavelet domain and discuss how this idea can be used to improve the security of watermarking schemes. Two methods to create random wavelet packet trees are discussed and analyzed. The security against unauthorized detec...

This paper presents a novel wavelet-based denoising and compression statistical model for 3D hippocampus shapes. Shapes are encoded using spherical wavelets and the objective is to remove noisy coefficients while keeping significant shape information. To do so, we develop a non-linear wavelet shrinkage model based on a data-driven Bayesian framework. We threshold wavelet coefficients by locally...

Denoising of images corrupted by Gaussian noise using wavelet transform is of great concern in the past two decades. In wavelet denoising method, detail wavelet coefficients of noisy image are thresholded using a specific thresholding function by comparing to a specific threshold value, and then applying inverse wavelet transform, results in denoised image. Recently, an effective image denoisin...

This paper reports a new reading for wavelets, which is based on the classical ’De Broglie’ principle. The waveparticle duality principle is adapted to wavelets. Every continuous basic wavelet is associated with a proper probability density, allowing defining the Shannon entropy of a wavelet. Further entropy definitions are considered, such as Jumarie or Renyi entropy of wavelets. We proved tha...

The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms, the wavelet transforms, which are every bit as useful as the Fourier transform. Wavelet transforms are used to expose the multi-scale structure of a signal an...

The image de-noising naturally corrupted by noise is a classical problem in the field of signal or image processing. Additive random noise can easily be removed using simple threshold methods. De-noising of natural images corrupted by Gaussian noise using wavelet techniques are very effective because of its ability to capture the energy of a signal in few energy transform values. The wavelet de...

Sets Ω in d-dimensional Euclidean space are constructed with the property that the inverse Fourier transform of the characteristic function 1Ω of the set Ω is a single dyadic orthonormal wavelet. The iterative construction is characterized by its generality, its computational implementation, and its simplicity. The construction is transported to the case of locally compact abelian groups G with...

In this paper, we consider the asymptotic behaviour of M-band scaling functions of Daubechies type as M tends to innnity.

Group here always means a locally compact Hausdorff group, subgroup means a closed subgroup. Let G be a group, H a subgroup and G/H the locally compact homogeneous space of left cosets x = xH. We denote by $(G) [®(G/H)] the family of all compact subsets of G [G/H], The group G acts on G/H in a natural way. If X C.G and Y QG/H, write XY for the set of all elements xy, x £ I , j £ Y. Now assume t...

A brief survey of a paper by Peter Steffen, et al. Introduction G.K. Chesterton, an English author and journalist from the turn of the century, once stated he desired to write a story about a man setting sail from England in search of a new and foreign land. Eventually, when the man reached the island of his destination, he found it to be the most extraordinary and fascinating place. Unbeknowns...