We propose a Bayesian method for complex amplitude estimation in low-rank interference. We assume that the received signal follows the generalized multivariate analysis of variance (GMANOVA) patterned-mean structure and is corrupted by low-rank spatially correlated interference and white noise. An iterated conditional modes (ICM) algorithm is developed for estimating the unknown complex signal amplitudes and interference and noise parameters. We also discuss initialization of the ICM algorithm and propose a (non-Bayesian) adaptive-matched-filter (AMF) signal detector that utilizes the ICM estimation results. Numerical simulations demonstrate the performance of the proposed methods