This paper exploits the interband correlations of color and multispectral images for wavelet-based denoising. For this, a multispectral extension of the linear minimum mean squared error estimation (LMMSE) is constructed to estimate the signal from the observed wavelet coefficients. The calculation involves the signal autocovariance matrices, which are estimated globally or locally for centered square windows using Maximum Likelihood and MAP. The method is demonstrated to outperform single-band denoising on color and 7-band Landsat multispectral images.