Topic
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.
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TL;DR: A new method for blind source separation (BSS) of nonstationary signals modeled as linear instantaneous mixtures of surface EMG signals based on whitening of the observations and rotation of the whitened observations resulted in better performance than previous methods for the separation of non stationary myoelectric signals.
Abstract: Surface electromyography (EMG) signals detected over the skin surface may be mixtures of signals generated by many active muscles due to poor spatial selectivity of the recording. In this paper, we propose a new method for blind source separation (BSS) of nonstationary signals modeled as linear instantaneous mixtures. The method is based on whitening of the observations and rotation of the whitened observations. The rotation is performed by joint diagonalization of a set of spatial wavelet distributions (SWDs). The SWDs depend on the selection of the mother wavelet which can be defined by unconstrained parameters via the lattice parameterization within the multiresolution analysis framework. As the sources are classically supposed to be mutually uncorrelated, the design parameters of the mother wavelet can be blindly optimized by minimizing the average (over time lags) cross correlation between the estimated sources. The method was tested on simulated and experimental surface EMG signals and results were compared with those obtained with spatial time-frequency distributions and with second-order statistics (only spectral information). On a set of simulated signals, for 10-dB signal-to-noise ratio (SNR), the cross-correlation coefficient between original and estimated sources was 0.92plusmn0.07 with wavelet optimization, 0.74plusmn0.09 with the wavelet leading to the poorest performance, 0.85plusmn0.07 with Wigner-Ville distribution, 0.86plusmn0.07 with Choi-Williams distribution, and 0.73plusmn0.05 with second-order statistics. In experimental conditions, when the flexor carpi radialis and pronator teres were concomitantly active for 50% of the time, crosstalk was 55.2plusmn10.0% before BSS and was reduced to 15.2plusmn6.3% with wavelet optimization, 30.1plusmn15.0% with the worst wavelet, 28.3plusmn12.3% with Wigner-Ville distribution, 26.2plusmn12.0% with Choi-Williams distribution, and 35.1plusmn15.5% with second-order statistics. In conclusion, the proposed approach resulted in better performance than previous methods for the separation of nonstationary myoelectric signals.
43 citations
TL;DR: A new method of estimating both biorthogonal compactly supported as well as semi-orthogonal infinitely/compactly supported wavelet from a given signal based on maximizing projection of the given signal onto successive scaling subspace results in minimization of energy of signal in the wavelet subspace.
43 citations
10 Apr 1997
TL;DR: In this article, the authors presented the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems, including the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems and for parametrization of Arnold-Weinstein curves in Floer variational approach.
Abstract: In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parametrized by the solutions of two reduced algebraical problems, one is nonlinear and the second is some linear problem, which is obtained from one of the next wavelet constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the method of Connection Coefficients. According to the orbit method and by using construction from the geometric quantization theory we construct the symplectic and Poisson structures associated with generalized wavelets by using metaplectic structure. We consider wavelet approach to the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems and for parametrization of Arnold-Weinstein curves in Floer variational approach.
43 citations
TL;DR: In this article, a wavelet application to the vibration-based damage evaluation technique is introduced, which requires only a few of the lower mode shapes before and after a small damage event in order to detect, locate, and size damage on plate-like structures.
43 citations
27 Apr 1993
TL;DR: The authors define a frame multiresolution analysis (FMRA) and provide a necessary and sufficient condition for constructing frames of translates that are part of the theoretical background for multiscale signal processing problems including filter bank design.
Abstract: A generalization of multiresolution analysis (MRA) to arbitrary affine frames, and the constructions of affine frames based on MRAs are considered and characterized. The authors define a frame multiresolution analysis (FMRA) and provide a necessary and sufficient condition for constructing frames of translates. Conditions for constructing FMRAs and associated frames are derived. The results are part of the theoretical background for multiscale signal processing problems including filter bank design, where redundancy and robustness play a role. >
43 citations