In this paper, we study denoising of multicomponent images. We present a framework of spatial wavelet-based denoising techniques, based on Bayesian least-squares optimization procedures, using prior models for the wavelet coefficients that account for the correlations between the image components. Within this framework, multicomponent prior models for the wavelet coefficients are required that a) fully account for the interband correlations between the image components, and b) approximate well the marginal distributions of the wavelet coefficients. For this, multicomponent heavy tailed models are applied. We analyze three mixture priors: Gaussian scale mixture (GSM) models, Laplacian mixture models and Bernoulli-Gaussian mixture models. As an extension of the Bayesian framework, we propose a framework that also accounts for the correlation between the multicomponent image and an auxiliary noise-free image, in order to improve the SNR of the first. For this, a GSM prior model was applied. Experiments are conducted in the domain of remote sensing in both, simulated and real noisy conditions.