  A sample-relaxed two-dimensional color principal component analysis
(SR-2DCPCA) approach is presented for face recognition and image reconstruction
based on quaternion models. A relaxation vector is automatically generated
according to the variances of training color face images with the same label. A
sample-relaxed, low-dimensional covariance matrix is constructed based on all
the training samples relaxed by a relaxation vector, and its eigenvectors
corresponding to the $r$ largest eigenvalues are defined as the optimal
projection. The SR-2DCPCA aims to enlarge the global variance rather than to
maximize the variance of the projected training samples. The numerical results
based on real face data sets validate that SR-2DCPCA has a higher recognition
rate than state-of-the-art methods and is efficient in image reconstruction.
