Modified robust image alignment by sparse and low rank decomposition for highly linearly correlated data

This paper proposes an effective and robust algorithm for image alignment on a set of linearly correlated ata. The new algorithm modifies the Robust Algorithm for Sparse and Low rank decomposition (RASL) by utilizing the prior information of partial column rank. To attain this, an extra term is incorporated in the decomposition of data matrix, which enables the new approach to be more resilient to errors, outliers and occlusions. The problem is cast as a constrained optimization problem, which is then solved by convex program. A new set of equations are also derived to update the variables involved in a round-robin manner. Conducted simulations on the recovery of aligned face images and handwritten digits reveal the effectiveness of the new algorithm compared with the main state-of-the-art works.