Tikhonov Regularization of Circle-Valued Signals
This addresses the processing of cyclic signals like phases or angles for applications in imaging and signal analysis, but it is incremental as it builds on existing Tikhonov regularization methods.
The authors tackled the problem of smoothing or interpolating circle-valued signals on arbitrary graphs by proposing a convex relaxation of a Tikhonov-type regularization model as a semidefinite program, and they developed an efficient algorithm to solve it.
It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to smoothen or interpolate circle-valued signals defined on arbitrary graphs. We propose a convex relaxation of this nonconvex problem as a semidefinite program, and an efficient algorithm to solve it.