A REAL STRUCTURE-PRESERVING ALGORITHM FOR THE LOW- RANK DECOMPOSITION OF PURE IMAGINARY QUATERNION MATRICES AND ITS APPLICATIONS IN SIGNAL PROCESSING

Abstract

With the increasing use of quaternions in fields such as quantum mechanics, rigid body rotation, signal and color image processing, and aerospace engineering, three- dimensional signal models represented by pure imaginary quaternion matrices have been cre- ated. This model treats the 3D information as a whole, and the processing preserves the intrinsic connections between the different channels. However, the computational process of quaternion algebra often generates real parts, which are inevitable. How to ensure the pure imaginary properties of 3D signal models is also a research priority. In this paper, we inves- tigate the low-rank decomposition of pure imaginary quaternion matrices using least squares iteration and give a real structure-preserving algorithm for the low-rank decomposition based on the isomorphic real representation. In addition, this matrix decomposition algorithm is applied to color image compression and 3D wave signal denoising problems. Numerical ex- periments show the effectiveness of the algorithm in this paper.