wmulden - PCA and Wavelet Denosining

I do not understand how PCA is used in the wmulden multivariate wavelet denoising function.

Can someone explain in layman's terms how PC are used in the wmulden wavelet function. I understand PCA etc., but not how this function applies it to wavelet denoising.

[Ali Mehr]

Actually PCA is all the reason why Multivariate denoising is working using wavelet. The whole basis of this module comes from a study of Aminghafari et al. (2006). They have used a study called "Multiscale PCA with application to multivariate statistical process monitoring" in order to denoise multivariate signals using wavelet and PCA. What PCA doese here, is to find the underlying function of a multivariate signal denoised by wavelet. As you know wavelet is a univariate denoising algorithm. They made this technique to use decomposition and denoising feature of wavelet and power of extracting the main feature of PCA. If you want to know what is the best number for your principal components, offerd by Aminghafari et al.(2006) you may use Kaiser criterion, it's easy and implanted in wmulden itself. Just use this: npc_app = 'kais'; npc_fin = 'kais'; then perform the process, and at the end ask for this: (e.g.) npc

npc = 2 2

I hope you may find this information useful.

[Megha S Kumar]

Hi, i am trying to implement wmspca inbuilt function step by step and compare it with eigen vectors in Wavelet Analyzer app also. when i input a 1024 x 4 signal matrix and apply 5 level dwt on each column. If i choose 1 principal component how can i reconstruct using inverse dwt as wavelet coefficients length and eigen vector lengths are totally different?.

Any help is appreciated. Thanks in advance.