On closed‐form solutions to the 4D nearest rotation matrix problem

In this paper, we address the problem of restoring orthogonality a numerically noisy 4D rotation matrix by finding its nearest (in Frobenius norm) correct matrix. This can be straightforwardly solved using Singular Value Decomposition (SVD). Nevertheless, to avoid numerical methods, present two new closed-form methods. One relies on direct minimization mentioned norm, and other passage double quaternion representation. A comparison these methods with respect SVD reveals that method based representation is superior in all aspects.