Convex Quaternion Optimization for Signal Processing: Theory and Applications

We present several discriminant theorems for convex quaternion functions analogous to their complex counterparts. We also provide several discriminant criteria for strongly convex functions by the theorems of convex quaternion functions. Furthermore, we prove that the quaternion Newton method can converge in one step for positive definite quadratic quaternion functions and provide two applications in quaternion signal processing. These results provide a solid theoretical foundation for convex quaternion optimization and open avenues for further developments in quaternion signal processing applications.
Source: IEEE Transactions on Signal Processing - Category: Biomedical Engineering Source Type: research