Quaternion Hierarchical Orthogonal Matching Pursuit

Quaternion orthogonal matching pursuit (QOMP) has been widely concerned for its good performance in color image representation, which selects the most correlated atom in each iteration. There is an underlying assumption that the correlated atoms of each test sample come from the same subspace. However, those atoms obtained by QOMP at each step may not be guaranteed to always originate from the same subspace, which will potentially affect the accuracy of this algorithm. In this paper, a quaternion hierarchical orthogonal matching pursuit (QHOMP) algorithm is proposed, which can overcome the limitation of identifying indexes with low correlation during in each iteration, thus selecting atoms that are not belong to the same class. Besides, QHOMP adopts the quaternion representation for color images, which can fully utilize the multiple channel information of each color image. We also provide a complete optimization process to overcome the non-commutativity of quaternion multiplication. The experimental results show the effectiveness of QHOMP for color face recognition in standard datasets.