New robust principal component analysis for joint image alignment and recovery via affine transformations, Frobenius and \(L_{2,1}\) norms (Q779978)

Summary: This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and \(L_{2,1}\) norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and \(L_{2,1}\) norms. To attain this, affine transformations and Frobenius and \(L_{2,1}\) norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works.