Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.

A New Wavelet Denoising Method for Selecting Decomposition Levels and Noise Thresholds

Abstract: A new method is presented to denoise 1-D experimental signals using wavelet transforms. Although the state-of-the-art wavelet denoising methods perform better than other denoising methods, they are not very effective for experimental signals. Unlike images and other signals, experimental signals in chemical and biophysical applications, for example, are less tolerant to signal distortion and under-denoising caused by the standard wavelet denoising methods. The new method: 1) provides a method to select the number of decomposition levels to denoise; 2) uses a new formula to calculate noise thresholds that does not require noise estimation; 3) uses separate noise thresholds for positive and negative wavelet coefficients; 4) applies denoising to the approximation component; and 5) allows the flexibility to adjust the noise thresholds. The new method is applied to continuous wave electron spin resonance spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion. In addition, its computation time is more than six times faster.

Non-Equispaced Fast Fourier Transforms with Applications to Tomography

Abstract: In this article we describe a non-equispaced fast Fourier transform. It is similar to the algorithms of Dutt and Rokhlin and Beylkin but is based on an exact Fourier series representation. This results in a greatly simplified analysis and increased flexibility. The latter can be used to achieve more efficiency. Accuracy and efficiency of the resulting algorithm are illustrated by numerical examples. In the second part of the article the non-equispaced FFT is applied to the reconstruction problem in Computerized Tomography. This results in a different view of the gridding method of O’Sullivan and in a new ultra fast reconstruction algorithm. The new reconstruction algorithm outperforms the filtered backprojection by a speedup factor of up to 100 on standard hardware while still producing excellent reconstruction quality.

Introduction to Wavelet Analysis

Abstract: Wavelet transform and multiresolution decomposition are described. Examples of the application of orthogonal wavelet transform to acoustic evoked potentials and otoacoustic emissions (OEA) are given and basic features of wavelet packets and wavelet network methods are characterized. An approach that enables the identification of local signal structures - a generalization of wavelet transform called Matching Pursuit - is presented. In the framework of this method the signal is decomposed into time-frequency ‘atoms', which offers a possibility of determination of an ‘instantaneous frequency’ with the accuracy close to the theoretical limit. The method is illustrated by application to OAE signals. The advantages and limitations of the methods presented are discussed.