The interferometry problem addresses the estimation of an unknown quantity exploiting the interference among measurements from different sources. These measurements are obtained from the Fourier domain but are sparse and contaminated with noise. We propose a parametric, sum-of-basis, model for these observations together with a Bayesian approach for reconstructing interferometry images. Our main contributions are the construction of a model with a complex-valued noise source, an implementation of an approximate inference method to train the model using Markov chain Monte Carlo and a quantitative comparison against the so-called dirty algorithm, where the proposed approach outperformed the considered baseline.