Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

On the correlation structure of the wavelet coefficients of fractional Brownian motion

Abstract: Shows that the interdependence of the discrete wavelet coefficients of fractional Brownian motion, defined by normalized correlation, decays exponentially fast across scales and hyperbolically fast along time. >

Wavelet-based enhancement of lung and bowel sounds using fractal dimension thresholding-part I: methodology

Abstract: An efficient method for the enhancement of lung sounds (LS) and bowel sounds (BS), based on wavelet transform (WT), and fractal dimension (FD) analysis is presented in this paper. The proposed method combines multiresolution analysis with FD-based thresholding to compose a WT-FD filter, for enhanced separation of explosive LS (ELS) and BS (EBS) from the background noise. In particular, the WT-FD filter incorporates the WT-based multiresolution decomposition to initially decompose the recorded bioacoustic signal into approximation and detail space in the WT domain. Next, the FD of the derived WT coefficients is estimated within a sliding window and used to infer where the thresholding of the WT coefficients has to happen. This is achieved through a self-adjusted procedure that iteratively "peels" the estimated FD signal and isolates its peaks produced by the WT coefficients corresponding to ELS or EBS. In this way, two new signals are constructed containing the useful and the undesired WT coefficients, respectively. By applying WT-based multiresolution reconstruction to these two signals, a first version of the desired signal and the background noise is provided, accordingly. This procedure is repeated until a stopping criterion is met, finally resulting in efficient separation of the ELS or EBS from the background noise. The proposed WT-FD filter introduces an alternative way to the enhancement of bioacoustic signals, applicable to any separation problem involving nonstationary transient signals mixed with uncorrelated stationary background noise. The results from the application of the WT-FD filter to real bioacoustic data are presented and discussed in an accompanying paper.

Denoising Techniques With Change-Point Approach for Wavelet-Based Power-Quality Monitoring

Abstract: A wavelet-transform (WT)-based power-quality (PQ) monitoring system captures voltage and current waveforms, when magnitudes of WT coefficients exceed the set threshold values across the scales. A lot of literatures has proposed several methods based on WT to detect and classify PQ disturbances. But a problem in the practical implementation of the wavelet-based triggering method is the presence of noise, riding on the signal. The presence of noise not only degrades the detection capability of wavelet-based PQ monitoring systems but also hinders the recovery of important information from the captured waveform for time localization and classification of the disturbances. Therefore, to enhance the performance of WT-based monitoring systems and to improve the classification accuracy of WT-based classifiers, two standard statistical hypothesis test-based denoising procedures have been proposed in this paper. Extensive tests conducted on the data obtained from simulations of a practical distribution system confirm the effectiveness of the proposed approaches in denoising of the PQ waveforms.

Sharpening of very high resolution images with spectral distortion minimization

Abstract: This work presents a viable solution to the problem of merging a multispectral image with an arbitrary number of bands with a higher resolution panchromatic observation. The proposed method relies on the generalized Laplacian pyramid, which is a multiscale oversampled structure in which spatial details are mapped on different scales. The goal is to selectively perform spatial-frequencies spectrum substitution from an image to another with the constraint of thoroughly retaining the spectral information of the coarser data. To this end, a vector injection model has been defined: at each pixel, the detail vector to be added is always parallel to the approximation. Furthermore, its components are scaled by factors measuring the ratio of local gains between the multispectral and panchromatic data. Such a model is calculated at a coarser resolution where both types of data are available and extended to the finer resolution by embedding the modulation transfer function of the multispectral scanner into the multiresolution analysis. In this way, the interband structure model can be extended to the higher resolution without the drawback of the poor enhancement occurring when the model assumes MTFs close to be ideal. Results are presented and discussed on very high resolution QuickBird data of an urban area.