The problem of estimating the power spectra of non-stationary stochastic processes by using the harmonic wavelet transform is addressed in this paper. Conventional spectral analysis provides spectral coefficients that are averaged over time and thus, does not represent the evolutionary behavior of power spectra of non-stationary processes. In this study, evolutionary power spectrum of a non-sta...

Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation.   Introduction: The...

Image fusion is to reduce uncertainty and minimize redundancy. It is a process of combining the relevant information from a set of images, into a single image, wherein the resultant fused image will be more informative and complete than any of the input images. Till date the image fusion techniques were like DWT or pixel based. These conventional techniques were not that efficient and they did ...

This paper presents a new approach to integrate and enhance registered multi-frame images with varied focuses simultaneously. The objective is to combine the information of multiple images from the same scene and then generate an image that is more suitable for human and machine perception or further image-processing tasks than its original sources. To enhance the integrated image, Smoothing Fi...

Standard DWT (Discrete Wavelet Transform), being non-redundant, is a very powerful tool for many non-stationary Signal Processing applications, but it suffers from three major limitations; 1) shift sensitivity, 2) poor directionality, and 3) absence of phase information. To reduce these limitations, many researchers developed real-valued extensions to the standard DWT such as WP (Wavelet Packet...

Well logging is an important tool for the characterization of subsurface rocks, being commonly used in the study of reservoir geology. It is well known that signals obtained as responses from geological media contain noise that can affect their interpretation, and that wavelet transform is more suitable than the Fourier transform to denoise non-stationary signals, as the ones obtained from well...

Several algorithms are reviewed for computing various types of wavelet transforms: the Mallat algorithm, the “a trous” algorithm and their generalizations by Shensa. The goal is 1) to develop guidelines for implementing discrete and continuous wavelet transforms efficiently, 2) to compare the various algorithms obtained and give an idea of possible gains by providing operation counts. The compu...

In this paper we study a generalization of the Donoho-Johnstone denoising model for the case of the translation invariant wavelet transform. Instead of soft-thresholding coeecients of the classical orthogonal discrete wavelet transform, we study soft-thresholding of the co-eecients of the translation invariant discrete wavelet transform. This latter transform is not an orthogonal transformation...