  Regression analysis-based approaches have been widely studied for face
recognition (FR) in the past several years. More recently, to better deal with
some difficult conditions such as occlusions and illumination, nuclear norm
based matrix regression methods have been proposed to characterize the low-rank
structure of the error image, which generalize the one-dimensional, pixel-based
error model to the two-dimensional structure. These methods, however, are
inherently devised for grayscale image based FR and without exploiting the
color information which is proved beneficial for FR of color face images.
Benefiting from quaternion representation, which is capable of encoding the
cross-channel correlation of color images, we propose a novel color FR method
by formulating the color FR problem as a nuclear norm based quaternion matrix
regression (NQMR). We further develop a more robust model called R-NQMR by
using the logarithm of the nuclear norm, instead of the original nuclear norm,
which adaptively assigns weights on different singular values, and then extend
it to deal with the mixed noise. The proposed models, then, are solved using
the effective alternating direction multiplier method (ADMM). Experiments on
several public face databases demonstrate the superior performance and efficacy
of the proposed approaches for color FR, especially for some difficult
conditions (occlusion, illumination and mixed noise) over some state-of-the-art
regression analysis-based approaches.
