Denoising of Sphere- and SO(3)-Valued Data by Relaxed Tikhonov Regularization
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Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, Condat (IEEE Trans. Signal Proc.) proposed a convex relaxation of the Tikhonov-regularized nonconvex problem for denoising circle-valued data. Using Schur complement arguments, we show that this variational model can be simplified while leading to the same solution. Our 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 minimizers to demonstrate the denoising behavior of the proposed approach.
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