Quaternion Optimization

Quaternion optimization focuses on solving optimization problems where the variables are quaternions, a mathematical extension of complex numbers useful for representing rotations and orientations in 3D space. Current research emphasizes developing efficient algorithms for various applications, including robust tensor completion for video inpainting, principal component analysis for color image processing, and hand-eye calibration in robotics, often employing techniques like matrix factorization, and generalized ridge regression. These advancements improve the accuracy and efficiency of solutions in diverse fields, offering significant benefits for computer vision, signal processing, and robotics.