We propose to extend the marginalized denoising autoencoder (MDA) framework with a domain regularization whose aim is to denoise both the source and target data in such a way that the features become domain invariant and the adaptation gets easier. The domain regularization, based either on the maximum mean discrepancy (MMD) measure or on the domain prediction, aims to reduce the distance between the source and the target data. We also exploit the source class labels as another way to regularize the loss, by using a domain classifier regularizer. We show that in these cases, the noise marginalization gets reduced to solving either the linear matrix system AX = B, for which there exists a closed-form solution, or to a Sylvester linear matrix equation AX + XB = C that can be solved efficiently using the Bartels-Stewart algorithm. We did an extensive study on how these regularization terms improve the baseline performance and we present experiments on three image benchmark datasets, conventionally used for domain adaptation methods. We report our findings and comparisons with state-of-the-art methods.