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.

Wavelet transform analysis of heart rate variability during myocardial ischaemia.

Abstract: Analysis of heart rate variability (HRV) is a valuable, non-invasive method for quantifying autonomic cardiac control in humans. Frequency-domain analysis of HRV involving myocardial ischaemic episodes should take into account its non-stationary behaviour. The wavelet transform is an alternative tool for the analysis of non-stationary signals. Fourteen patients have been analysed, ranging from 40 to 64 years old and selected from the European Electrocardiographic ST-T Database (ESDB). These records contain 33 ST episodes, according to the notation of the ESDB, with durations of between 40s and 12min. A method for analysing HRV signals using the wavelet transform was applied to obtain a time-scale representation for very low-frequency (VLF), low-frequency (LF) and high-frequency (HF) bands using the orthogonal multiresolution pyramidal algorithm. The design and implementation using fast algorithms included a specially adapted decomposition quadrature mirror filter bank for the frequency bands of interest. Comparing a normality zone against the ischaemic episode in the same record, increases in LF (0.0112±0.0101 against 0.0175±0.0208s2Hz−1; p<0.1) and HF (0.0011±0.0008 against 0.0017±0.0020s2Hz−1; p<0.05) were obtained. The possibility of using these indexes to develop an ischaemic-episode classifier was also tested. Results suggest that wavelet analysis provides useful information for the assessment of dynamic changes and patterns of HRV during myocardial ischaemia.

BLaC-Wavelets: a multiresolution analysis with non-nested spaces

Abstract: In the last five years, there has been numerous applications of wavelets and multiresolution analysis in many fields of computer graphics as different as geometric modelling, volume visualization or illumination modelling. Classical multiresolution analysis is based on the knowledge of a nested set of functional spaces in which the successive approximations of a given function converge to that function, and can be efficiently computed. This paper first proposes a theoretical framework which enables multiresolution analysis even if the functional spaces are not nested, as long as they still have the property that the successive approximations converge to the given function. Based on this concept, we finally introduce a new multiresolution analysis with exact reconstruction for large data sets defined on uniform grids. We construct a one-parameter family of multiresolution analyses which is a blending of Haar and linear multiresolution, using BLaC (Blending of Linear and Constant) wavelets.

Continuous wavelet decompositions, multiresolution, and contrast analysis

Abstract: A continuous version of multiresolution analysis is described, starting from usual continuous wavelet decompositions. Scale discretization leads to decomposition into functions of arbitrary bandwidth, satisfying QMF-like conditions. Finally, a nonlinear multiresolution scheme is described, providing multiplicative reconstruction formulas.

Spike Detection and Clustering With Unsupervised Wavelet Optimization in Extracellular Neural Recordings

Abstract: Automatic and accurate detection of action potentials of unknown waveforms in noisy extracellular neural recordings is an important requirement for developing brain–computer interfaces. This study introduces a new, wavelet-based manifestation variable that combines the wavelet shrinkage denoising with multiscale edge detection for robustly detecting and finding the occurrence time of action potentials in noisy signals. To further improve the detection performance by eliminating the dependence of the method to the choice of the mother wavelet, we propose an unsupervised optimization for best basis selection. Moreover, another unsupervised criterion based on a correlation similarity measure was defined to update the wavelet selection during the clustering to improve the spike sorting performance. The proposed method was compared to several previously proposed methods by using a wide range of realistic simulated data as well as selected experimental recordings of intracortical signals from freely moving rats. The detection performance of the proposed method substantially surpassed previous methods for all signals tested. Moreover, updating the wavelet selection for the clustering task was shown to improve the classification performance with respect to maintaining the same wavelet as for the detection stage.

Multiresolution analysis in extraction of reference lines from documents with gray level background

Abstract: Based on wavelets, a theoretical method has been developed to process multi-gray level documents. In this method, two-dimensional multiresolution analysis, a wavelet decomposition algorithm, and compactly supported orthonormal wavelets are used to transform a document image into sub-images. According to these sub-images, the reference lines of a multi-gray level document can be extracted, and knowledge about the geometric structure of the document can be acquired. Particularly, this approach is more efficient to process form documents with gray level background. Experiments indicate that this new method can be applied to process documents with promising results.