Nonconvex Rank Relaxations based Matrix Regression for Face Reconstruction and Recognition

As we know, nuclear norm based matrix regression (NMR) methods have the popular applications to face reconstruction and recognition with occlusion and illumination changes. However, when facing larger occlusions and heavier illuminations in real-world applications, these methods usually can not work well due to the biased estimator of nuclear norm as the rank relaxation. To overcome this issue, noconvex matrix regression approaches are presented by generalized nonconvex rank relaxations derived from several to-norm substitutes, to characterize the low-rank structure of the residual image matrix. The representation coefficient vectors can be achieved with the help of nonconvex and even multi-variables alternating direction method of multipliers (ADMM) with theoretical analysis to optimize the developed problems and guarantee the closed-form solution of each subproblem, synchronously. Moreover, we design the minimal representation formula for the residual matrix as a decision rule. Finally, experimental results on face reconstruction and recognition can show the superiority of the proposed methodologies over the mostly related matrix regression methods including Li-norm and l2-norm regularized NMR methods.