  Manifold-valued signal- and image processing has received attention due to
modern image acquisition techniques. Recently, a convex relaxation of the
otherwise nonconvex Tikhonov-regularization for denoising circle-valued data
has been proposed by Condat (2022). The circle constraints are here encoded in
a series of low-dimensional, positive semi-definite matrices. Using Schur
complement arguments, we show that the resulting variational model can be
simplified while leading to the same solution. The simplified model can be
generalized to higher dimensional spheres and to SO(3)-valued data, where we
rely on the quaternion representation of the latter. Standard algorithms from
convex analysis can be applied to solve the resulting convex minimization
problem. As proof-of-the-concept, we use the alternating direction method of
multipliers to demonstrate the denoising behavior of the proposed method. In a
series of experiments, we demonstrate the numerical convergence of the signal-
or image values to the underlying manifold.
