Multispectral data restoration by the wavelet Karhunen-Loeve transform

We introduce in this paper the notion of wavelet Karhunen-Loeve transform (WT-KLT) and apply it to the problem of noise removal. Decorrelating first the data in the spatial domain using the WT and afterwards using the KLT in spectral domain allows us to derive a robust noise modeling in the WT-KLT space, and hence to filter the transformed data in an efficient way. Experiments are performed in order to derive (i) the best way to calculate the covariance matrix in the case of noisy data, (ii) the best method to correct the noisy WT-KLT coefficients. Finally, we investigate if the curvelet transform could be an alternative to the wavelet transform for color image filtering. (C) 2001 Elsevier Science B.V. All rights reserved.