Sparse Subspace Clustering for Incomplete Images

In this paper, we propose a novel approach to cluster incomplete images leveraging sparse subspace structure and total variation regularization. Sparse subspace clustering obtains a sparse representation coefficient matrix for input data points by solving an ℓ₁ minimization problem, and then uses the coefficient matrix to construct a sparse similarity graph over which spectral clustering is performed. However, conventional sparse subspace clustering methods are not exclusively designed to deal with incomplete images. To this end, our goal in this paper is to simultaneously recover incomplete images and cluster them into appropriate clusters. A new nonconvex optimization framework is established to achieve this goal, and an efficient first-order exact algorithm is developed to tackle the nonconvex optimization. Extensive experiments carried out on three public datasets show that our approach can restore and cluster incomplete images very well when up to 30% image pixels are missing.