RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images

This paper studies the problem of simultaneously align-ing a batch of linearly correlated images despite gross cor-ruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of errors and a low-rank matrix of recovered aligned images. We reduce this extremely challenging op-timization problem to a sequence of convex programs that minimize the sum of ℓ1-norm and nuclear norm of the two component matrices, which can be efficiently solved by scal-able convex optimization techniques with guaranteed fast convergence. We verify the efficacy of the proposed ro-bust alignment algorithm with extensive experiments with both controlled and uncontrolled real data, demonstrating higher accuracy and efficiency than existing methods over a wide range of realistic misalignments and corruptions. 1