Low-rank based models are proved outstanding for denoising on the data with strong repetitive or redundant property. However, for natural images with complex structures or rich details, the performance drops down because of the weak low-rankness of the data. A feasible solution is to transform the data into a suitable domain to further explore the underlying low-rank information. In this paper, we present a novel approach to create such a domain via a fully replicated linear autoencoder network. By applying various low-rank models to the feature maps generated by the encoder rather than the original data, and then performing inverse transformation by the decoder, their denoising performances all get enhanced. In addition, feature maps also show good sparsity, hence we introduce a new measure combining sparse and low-rank regularity, and further propose corresponding single image denoising model. Extensive experiments show the superiority of our work.