Robust quaternion matrix completion with applications to image inpainting

Z Jia, MK Ng, GJ Song - Numerical Linear Algebra with …, 2019 - Wiley Online Library
Z Jia, MK Ng, GJ Song
Numerical Linear Algebra with Applications, 2019Wiley Online Library
In this paper, we study robust quaternion matrix completion and provide a rigorous analysis
for provable estimation of quaternion matrix from a random subset of their corrupted entries.
In order to generalize the results from real matrix completion to quaternion matrix
completion, we derive some new formulas to handle noncommutativity of quaternions. We
solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix
that is a convex surrogate for the quaternion matrix rank, and the ℓ 1‐norm of sparse …
Summary
In this paper, we study robust quaternion matrix completion and provide a rigorous analysis for provable estimation of quaternion matrix from a random subset of their corrupted entries. In order to generalize the results from real matrix completion to quaternion matrix completion, we derive some new formulas to handle noncommutativity of quaternions. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix that is a convex surrogate for the quaternion matrix rank, and the 1‐norm of sparse quaternion matrix entries. We show that, under incoherence conditions, a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and that the corrupted entries are sparsely located. The quaternion framework can be used to represent red, green, and blue channels of color images. The results of missing/noisy color image pixels as a robust quaternion matrix completion problem are given to show that the performance of the proposed approach is better than that of the testing methods, including image inpainting methods, the tensor‐based completion method, and the quaternion completion method using semidefinite programming.
Wiley Online Library
以上显示的是最相近的搜索结果。 查看全部搜索结果