We mainly study the low-rank image recovery problem by proposing a bilinear low-rank coding framework called Tensor Low-Rank Representation. For enhanced low-rank recovery and error correction, our method constructs a low-rank tensor subspace to reconstruct given images along row and column directions simultaneously by computing two low-rank matrices alternately from a nuclear norm minimization problem, so both column and row information of data can be effectively preserved. Our bilinear approach seamlessly integrates the low-rank coding and dictionary learning into a unified framework. Thus, our formulation can be treated as enhanced Inductive Robust Principal Component Analysis with noise removed by low-rank representation, and can also be considered as the enhanced low-rank representation with a clean informative dictionary via low-rank embedding. To enable our method to include outside images, the out-of-sample extension is also presented by regularizing the model to correlate image features with the low-rank recovery of the images. Comparison with other criteria shows that our model exhibits stronger robustness and enhanced performance. We also use the outputted bilinear low-rank codes for feature learning. Two unsupervised local and global low-rank subspace learning methods are proposed for extracting image features for classification. Simulations verified the validity of our techniques for image recovery, representation and classification. 
Bilinear low-rank coding framework and extension for robust image recovery and feature representation