Tensor form of GPBiCG algorithm for solving the generalized Sylvester quaternion tensor equations
Xin‐Fang Zhang, Wei Ding, Tao Li
Abstract
Sylvester quaternion tensor equations have a wide range of applications in image processing and system and control theory. In this paper, by the Kronecker product and vectorization operator and the properties of quaternion tensors, we focus mainly on proposing the tensor form of the generalized product-type biconjugate gradient method for solving generalized Sylvester quaternion tensor equations. As an application, we apply the proposed method to restore a blurred and noisy-free color video. The obtained numerical results illustrate the effectiveness of our method compared with some existing methods.
Topics & Concepts
Kronecker productQuaternionMathematicsSylvester equationVectorization (mathematics)Cartesian tensorTensor (intrinsic definition)Tensor contractionTensor productKronecker deltaAlgebra over a fieldApplied mathematicsMathematical analysisTensor densityComputer scienceTensor fieldExact solutions in general relativityPure mathematicsGeometryParallel computingQuantum mechanicsEigenvalues and eigenvectorsPhysicsTensor decomposition and applicationsSparse and Compressive Sensing TechniquesAdvanced Neuroimaging Techniques and Applications