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As a new color image representation tool, quaternion has achieved excellentresults in color image processing problems. In this paper, we propose a novellow-rank quaternion matrix completion algorithm to recover missing data ofcolor image. Motivated by two kinds of low-rank approximation approaches(low-rank decomposition and nuclear norm minimization) in traditionalmatrix-based methods, we combine the two approaches in our quaternionmatrix-based model. Furthermore, the nuclear norm of the quaternion matrix isreplaced by the sum of Frobenius norm of its two low-rank factor quaternionmatrices. Based on the relationship between quaternion matrix and itsequivalent complex matrix, the problem eventually is converted from quaternionnumber field to complex number field. An alternating minimization method isapplied to solve the model. Simulation results on real world color imagerecovery show the superior performance and efficiency of the proposed algorithmover some state-of-the-art tensor-based ones.

Color image recovery using low-rank quaternion matrix completion algorithm