arXiv subjects

Baohua Huang

Publications and source records attributed to Baohua Huang.

2 recordsLinked to original sources

arXiv2026

Structure preserving quaternion conjugate gradient-type methods for solving non-Hermitian quaternion linear systems

In this paper, we consider the non-Hermitian quaternion linear systems arising from color image restoration and three-dimensional signal filtering problems. For exploring to solve such systems, we present two innovative structure-preserving conjugate gradient-type methods, QNHERLQ and QNHERQR, which are based on the unitary equivalence transformations of the non-Hermitian quaternion matrices to tridiagonal forms, called quaternion Saunders-Simon-Yip tridiagonalization procedure. The proposed tridiagonalization procedure for non-Hermitian quaternion matrices is closely related to the quaternion Lanczos process for Hermitian matrices, and is very different from the quaternion Lanczos biorthogonalization process for non-Hermitian matrices. The convergence of QNHERLQ and QNHERQR is discussed, which depends on the singular values of the coefficient matrix. Also we show that both algorithms have the finite termination property and constant costs per iteration step. Numerical results illustrate that the proposed algorithms are with the robustness and effectiveness compared with QGMRES and QQMR.

math.NA↗

arXiv2024

Nonconvex Robust Quaternion Matrix Completion for Imaging Processing

One of the tasks in color image processing and computer vision is to recover clean data from partial observations corrupted by noise. To this end, robust quaternion matrix completion (QMC) has recently attracted more attention and shown its effectiveness, whose convex relaxation is to minimize the quaternion nuclear norm plus the quaternion $L_1$-norm. However, there is still room to improve due to the convexity of the convex surrogates. This paper proposes a new nonconvex robust QMC model, in which the nonconvex MCP function and the quaternion $L_p$-norm are used to enhance the low-rankness and sparseness of the low-rank term and sparse term, respectively. An alternating direction method of multipliers (ADMM) algorithm is developed to solve the proposed model and its convergence is given. Moreover, a novel nonlocal-self-similarity-based nonconvex robust quaternion completion method is proposed to handle large-scale data. Numerical results on color images and videos indicate the advantages of the proposed method over some existing ones.

math.NA↗