An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the L 2,1 Norms and Affine Transformation

Abstract

In this study, an effective robust PCA is developed for joint image alignment and recovery via $L_{\mathrm{2,1}}$ norms and affine transformations. To alleviate the potential impacts of outliers, heavy sparse noises, occlusions, and illuminations, the $L_{\mathrm{2,1}}$ norms along with affine transformations are taken into consideration. The determination of the parameters involved and the updating affine transformations is arranged in the form of a constrained convex optimization problem. To reduce the computation load, we also further decompose the error as sparse error and Gaussian noise; additionally, the alternating direction method of multipliers (ADMM) is considered to develop a new set of recursive equations to update the optimization parameters and the affine transformations iterative. The convergence of the derived updating equation is explained as well. Conducted simulations illustrate that the new method is superior to the baseline works in terms of precision on some public databases.