Quaternion Collaborative and Sparse Representation With Application to Color Face Recognition.

Collaborative representation-based classification (CRC) and sparse representation-based classification (SRC) have recently achieved great success in face recognition (FR). Previous CRC and SRC are originally designed in the real setting for grayscale image based FR. They represent the color channels of a query color image separately and ignore the structural correlation information among the color channels. To remedy this limitation, in this paper we propose two novel representationbased classification (RC) methods for color face recognition, namely quaternion collaborative representation-based classification (QCRC) and quaternion sparse representation-based classification (QSRC) using quaternion ℓ1 minimization. By modeling each color image as a quaternionic signal, they naturally preserve the color structures of both query and gallery color images while uniformly coding the query channel images in a holistic manner. Despite the empirical success of CRC and SRC on FR, few theoretical results are developed to guarantee their effectiveness. Another purpose of this paper is to establish the theoretical guarantee for QCRC and QSRC under mild conditions. Comparisons with competing methods on benchmark real-world databases consistently show the superiority of the proposed methods for both color face recognition and reconstruction.