# wmulden

Wavelet multivariate denoising

## Syntax

## Description

`[`

returns a denoised version `x_den`

,`npc`

,`nestcov`

,`dec_den`

,`pca_params`

,`den_params`

]
= wmulden(`x`

,`level`

,`wname`

,`npc_app`

,`npc_fin`

,`tptr`

,`sorh`

)`x_den`

of the input matrix
`x`

. The strategy combines univariate wavelet denoising in
the basis where the estimated noise covariance matrix is diagonal with noncentered
Principal Component Analysis (PCA) on approximations in the wavelet domain or with
final PCA.

`[dec,`

returns the wavelet decomposition `pca_params`

]
= wmulden("estimate",`dec`

,`npc_app`

,`npc_fin`

)`dec`

and the principal
components estimates `pca_params`

.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

The multivariate denoising procedure is a generalization of the one-dimensional strategy. It combines univariate wavelet denoising in the basis where the estimated noise covariance matrix is diagonal and non-centered Principal Component Analysis (PCA) on approximations in the wavelet domain or with final PCA.

The robust estimate of the noise covariance matrix given by the minimum covariance determinant estimator based on the matrix of finest details.

## References

[1] Aminghafari, Mina, Nathalie
Cheze, and Jean-Michel Poggi. “Multivariate Denoising Using Wavelets and Principal
Component Analysis.” *Computational Statistics & Data Analysis*
50, no. 9 (May 2006): 2381–98. https://doi.org/10.1016/j.csda.2004.12.010.

[2] Rousseeuw, Peter J., and
Katrien Van Driessen. “A Fast Algorithm for the Minimum Covariance Determinant
Estimator.” *Technometrics* 41, no. 3 (August 1999): 212–23.
https://doi.org/10.1080/00401706.1999.10485670.

## Version History

**Introduced in R2006b**