The quaternion wavelet transform is a new multiscale analysis tool. Firstly, this paper studies the standard orthogonal basis of scale space and wavelet space of quaternion wavelet transform in spatial L2 R2 , proves and presents quaternion wavelet’s scale basis function and wavelet basis function concepts in spatial scale space L2 R2;H , and studies quaternion wavelet transform structure. Fina...

• Why the wavelet coefficients were assumed independent and non-Gaussian [1, 2, 3, 4, 5]? Because of the WT primary properties: (locality, multiresolution and compression) and interpretation of the WT as a whitening process which attempts to make the coefficients statistically independent. • Why the coefficients are assumed jointly Gaussian [6, 7, 8]? Because it helps to captures the linear cor...

The main objective of this paper is to use ant optimized neural networks to generate artificial earthquake records. In this regard, training accelerograms selected according to the site geology of recorder station and Wavelet Packet Transform (WPT) used to decompose these records. Then Artificial Neural Networks (ANN) optimized with Ant Colony Optimization and resilient Backpropagation algorith...

Since the last decade the study of the wavelet transform has attracted many efforts and made great progresses. However, the research interest is still growing. In this thesis, we investigate the applications of the wavelet transform to image and video processing. We first study the wavelet transform mainly from a statistical point of view. Specifically, we study the statistics of the wavelet co...

This paper aims to study and compare the compression efficiencies of wavelet-bitmap and wavelet-Huffman. Both methods use wavelet to deduct a portion of the information in the image that can endure losing it without a significant disturbance in the image itself. Both methods deal with thresholding of wavelet coefficients to produce as much as possible zero coefficients for the purpose of higher...

This paper presents an embedded wavelet packet image coding algorithm which is based on context classification and quadtree ordering (CCAQO). To match up well with the quadtree-based embedded coder, a new cost function for the best basis selection is adopted in discrete wavelet packet transform (DWPT). In addition, combined with the structure of the best wavelet packet basis, a complete quadtre...

This paper is a contribution to the analysis of the statistical correlation of the wavelet packet coefficients resulting from the decomposition of a random process, stationary in the wide-sense, whose power spectral density is bounded with support in [−π, π]. Consider two quadrature mirror filters (QMF) that depend on a parameter r, such that these filters tend almost everywhere to the Shannon ...

Both wavelet denoising and denosing methods using the concept of sparsity are based on softthresholding. In sparsity based denoising methods, it is assumed that the original signal is sparse in some transform domains such as the wavelet domain and the wavelet subsignals of the noisy signal are projected onto `1-balls to reduce noise. In this lecture note, it is shown that the size of the `1-bal...

The objective of current work is to show the effectiveness of using wavelet transform for detection and localization of small damages. The spatial data used here are the mode shapes and strain energy data of the damaged plate. Because the wavelet coefficients are performed with various scale indices, local perturbations in the mode shapes and strain energy data can be found in the finer scale t...

This paper is concerned with the estimation and evaluation of wavelet coefficients of the composition F ◦u of two functions F and u from the wavelet coefficients of u. Our main objective is to show that certain sequence spaces that can be used to measure the sparsity of the arrays of wavelet coefficients are stable under a class of nonlinear mappings F that occur naturally, e.g., in nonlinear P...