This paper proposes a general method for dealing with the problem of recovering the low-rank structure, in which the data can be deformed by some unknown transformations and corrupted by sparse or nonsparse noises. Nonconvex penalization method is used to remedy the drawbacks of existing convex penalization method and a quadratic penalty is further used to better tackle the nonsparse noises in the data. We exploits the local linear approximation (LLA) method for turning the resulting nonconvex penalization problem into a series of weighted convex penalization problems and these subproblems are efficiently solved via the augmented Lagrange multiplier (ALM). Besides comparing with the method of robust alignment by sparse and low-rank decomposition for linearly correlated images (RASL), we also propose a nonconvex penalized lowrank and sparse decomposition (NLSD) model as comparison. Numerical experiments are conducted on both controlled and uncontrolled data to demonstrate the outperformance of the proposed method over RASL and NLSD.

This work was published on Science China Information Sciences (2016) pp.1-13.titled Nonconvex plus quadratic penalized low-rank and sparse decomposition for noisy image alignment.