Many unsupervised learning methods have been proposed to discover the structure of manifolds embedded in high-dimensional input spaces. However, image reconstruction requires mapping the learned low-dimension data in the feature space back to the input space, which can be challenging if the mapping function is implicit. This work presents an image reconstruction scheme closely related to machine learning methods learning manifolds via tangent space alignment. Here, the mapping transform is explicit and learned from the data. This model is a nonlinear generalization of the Low-Rank matrix/tensor model, reconstructing undersampled MR data with lower rank than the standard Low-Rank reconstruction.