In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an additive noise. In this paper, we address the problem of recovering the image components in a wavelet domain by adopting a variational approach. Our contribution is twofold. First, an appropriate multivariate penalty function is derived from a novel joint prior model of the probability distribution of the wavelet coefficients located at the same spatial position in a given subband through all the channels. Secondly, we address the challenging issue of computing the Maximum A Posteriori estimate by using a Majorize-Minimize optimization strategy. Simulation tests carried out on multispectral satellite images show that the proposed method outperforms conventional techniques.