Bilinear low-rank coding framework and extension for robust image recovery and feature representation

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. (C) 2015 Elsevier B.V. All rights reserved.