Bayesian reconstruction of trichromatic images using Cauchy priors in the wavelet domain

We seek a method to reconstruct mosaiced trichromatic images, using Bayesian methods in conjunction with a multivariate Cauchy prior. The Cauchy distribution is able to model the heavy-tailed distribution of spatial subband coefficients. Furthermore, the marginals of a multivariate Cauchy distribution are also Cauchy, making it useful for the color case where we must also capture correlations across sensors of different spectral classes. As proof of concept, we developed a method for spatially one-dimensional trichromatic images. Compared to an image estimate obtained via linear interpolation, the Cauchy-based Bayesian method has greater signal-to-noise ratio and exhibits reduced aliasing artifacts.