Quaternion Structure-preserving Method And Its Application In Color Face Recognition

The theory of quaternion was carved by William Rowan Hamilton in the 1840s to 1860s,is a non-commutative extension in four-dimensional space of complex field,plays an important role in theoretical research and scientific engineering computing problem.Since the multiplication of quaternion is non-commutative,quaternion oper-ations faced difficulties in slow calculation speed,is hard to compute with large scale quaternion matrix.The real representation method is one of the most commonly algo-rithms to solve quaternion matrix problem,however,the dimension of real representa-tion matrix is four times as quaternion matrix,it makes storage space and computation so expensive.In this paper,for quaternionic eigenvalue problem,we proposed a kind of structure-preserving method--structure-preserving Jacobi method,The basic idea of the algorithm is:take full advantage of JRS-symmetry of real representation matrix,tectonic structure-preserving Jacobi rotation,transform a 8 x 8 submatrix into a di-agonal form each step,make off-diagonal elements of whole matrix to zeros step by step while every iteration,get a diagonal matrix with the same JRS-symmetry finally.The algorithm takes full use of real operation to realize diagonalization in Hermitian quaternion matrix,with high accuracy,fast speed,small amount of storage space and computation.For quaternion real representation matrix,we proposed maximum el-ement structure-preserving Jacobi method and row cyclic structure-preserving Jacobi method,and presented the convergency analysis.Numerical experiments illustrate that,structure-preserving Jacobi method is better than classical Jacobi method in operation time、storage space and computation intensive readings.Finally,we apply structure-preserving Jacobi method to compute color faces’ eigenfaces,and deal with different expressions、blurrings、noises etcetera factors by using structure-preserving projec-tion for color faces’ recognition.