In practice, data gathered by wireless sensor networks often belongs in a low-dimensional subspace, but it can present missing as well as corrupted values due to sensor malfunctioning and/or malicious attacks. We study the problem of Maximum Likelihood estimation of the low-rank factors of the underlying structure in such situation, and develop an Expectation-Maximization algorithm to this purpose, together with an effective initialization scheme. The proposed method outperforms previous schemes based on an initial faulty sensor identification stage, and is competitive in terms of complexity and performance with convex optimization-based matrix completion approaches.