A Quaternion Framework for Robust Color Images Completion

In this paper, we study robust color images completion and provide a rigorous analysis for provable estimation of color images from a random subset of their corrupted pixels. Our analysis is focused on the use of quaternion framework as a representation of color images. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix which is a convex surrogate for a quaternion matrix rank, and the l1-norm of sparse quaternion matrix entries. We show that under incoherence conditions that a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and the corrupted entries are sparsely located. Numerical examples are presented to illustrate our theoretical results. The results of noisy color images completion are also given to show the performance of the proposed approach is better than the testing methods using the unfolding and performing image completion separately in each color channel.

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