Continuous wavelet transform based source separation

2007 ◽  
Author(s):  
Lee-Pierre Belley ◽  
Marcel Gabrea ◽  
Christian Gargour
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Source Separation ◽  
Continuous Wavelet

scholarly journals A New Approach for Motor Imagery Classification Based on Sorted Blind Source Separation, Continuous Wavelet Transform, and Convolutional Neural Network

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4541 ◽  
Author(s):  
César J. Ortiz-Echeverri ◽  
Sebastián Salazar-Colores ◽  
Juvenal Rodríguez-Reséndiz ◽  
Roberto A. Gómez-Loenzo
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Convolutional Neural Network ◽  
Blind Source Separation ◽  
Continuous Wavelet Transform ◽  
Signal To Noise Ratio ◽  
Brain Activity ◽  
Source Separation ◽  
Continuous Wavelet ◽  
Spectral Correlation

Brain-Computer Interfaces (BCI) are systems that allow the interaction of people and devices on the grounds of brain activity. The noninvasive and most viable way to obtain such information is by using electroencephalography (EEG). However, these signals have a low signal-to-noise ratio, as well as a low spatial resolution. This work proposes a new method built from the combination of a Blind Source Separation (BSS) to obtain estimated independent components, a 2D representation of these component signals using the Continuous Wavelet Transform (CWT), and a classification stage using a Convolutional Neural Network (CNN) approach. A criterion based on the spectral correlation with a Movement Related Independent Component (MRIC) is used to sort the estimated sources by BSS, thus reducing the spatial variance. The experimental results of 94.66% using a k-fold cross validation are competitive with techniques recently reported in the state-of-the-art.

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

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