Approximated RPCA for fast and efficient recovery of corrupted and linearly correlated images and video frames

This paper presents an approximated Robust Principal Component Analysis (ARPCA) framework for recovery of a set of linearly correlated images. Our algorithm seeks an optimal solution for decomposing a batch of realistic unaligned and corrupted images as the sum of a low-rank and a sparse corruption matrix, while simultaneously aligning the images according to the optimal image transformations. This extremely challenging optimization problem has been reduced to solving a number of convex programs, that minimize the sum of Frobenius norm and the l₁-norm of the mentioned matrices, with guaranteed faster convergence than the state-of-the-art algorithms. The efficacy of the proposed method is verified with extensive experiments with real and synthetic data.