Structure preserving quaternion full orthogonalization method with applications
Tao Li, Qing‐Wen Wang
Abstract
Abstract This article proposes a structure‐preserving quaternion full orthogonalization method (QFOM) for solving quaternion linear systems arising from color image restoration. The method is based on the quaternion Arnoldi procedure preserving the quaternion Hessenberg form. Combining with the preconditioning techniques, we further derive a variant of the QFOM for solving the linear systems, which can greatly improve the rate of convergence of QFOM. Numerical experiments on randomly generated data and color image restoration problems illustrate the effectiveness of the proposed algorithms in comparison with some existing methods.
Topics & Concepts
OrthogonalizationQuaternionMathematicsConvergence (economics)AlgorithmLinear systemRate of convergenceApplied mathematicsMathematical optimizationComputer scienceMathematical analysisGeometryKey (lock)EconomicsEconomic growthComputer securityMathematical Analysis and Transform MethodsSparse and Compressive Sensing TechniquesImage and Signal Denoising Methods