Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and groups acting on R n. We also show how this action can give rise to wavelets, and in particular, MSF wavelets)in L 2 (R n).

In geophysical exploration different types of measurements are used to probe the same subsurface region. In this paper we show that the wavelet transform can aid the process of linking different data types. The continuous wavelet transform, and in particular the analysis of amplitudes along wavelet transform modulus maxima lines, is a powerful tool to analyze the characteristic properties of lo...

During their service life, marine pipelines continually accumulate damage as a result of the action of various environmental forces. Clearly, the development of robust techniques for early damage detection is very important to avoid the possible occurrence of a disastrous structural failure. Most of vibration-based damage detection methods require the modal properties that are obtained from mea...

The major challenge in the wavelet transforms is that there exist different classes of wavelet filters for different kinds of applications. In this chapter, we propose a generalized lifting-based wavelet processor that can perform various forward and inverse Discrete Wavelet Transforms (DWTs) and Discrete Wavelet Packets (DWPs) that also supports higher order wavelet filters. Our architecture i...

introduction: one of the major problems in the development of nuclear medicine images is the presence of noise. the noise level in nuclear medicine images is usually reduced by the analysis of imaging data in a fourier transform environment. the main drawback of this environment belongs to low signal to noise ratio in high frequencies because removing noise frequencies may remove data and times...

Wavelet transforms have proven to be useful tools for several applications, including signal analysis, signal coding, and image compression. This paper surveys the VLSI architec-tures that have been proposed for computing the Discrete and Continuous Wavelet Transforms for 1-D and 2-D signals. The proposed architectures range from SIMD arrays to folded architectures such as systolic arrays and p...

A major step toward the use of hyperspectral sensors to detect subpixel targets is the ability to detect constituent absorption bands within a pixel’s hyperspectral curve. This paper introduces the use of multiresolution analysis, specifically wavelet transforms, for the automated detection of low amplitude and overlapping constituent bands in hyperspectral curves. The wavelet approach is evalu...

The theory of periodic wavelet transforms presented here was originally developed to deal with the problem of epileptic seizure prediction. A central theorem in the theory is the characterization of wavelets having time and scale periodic wavelet transforms. In fact, we prove that such wavelets are precisely generalized Haar wavelets plus a logarithmic term. It became apparent that the aforemen...

This paper concerns the issue of wavelet analysis of signals by continuous and discrete wavelet transforms (CWT – Continous Wavelet Transform, DWT – Discrete Wavelet Transform). The main goal of our work was to develop a program which, through the CWT and the DWT analyses, would obtain graph of time-scale changes and would transform it into the spectrum, that is a graph of frequency changes. In...