We introduce a general convexification framework for regularization of signals with values in a cyclic structure, such as angles, phases or hue values. These include the total cyclic variation, as well as cyclic versions of quadratic regularization, Huber-TV and Mumford-Shah regularity. The method handles the periodicity of values in a simple way, is invariant to cyclical shifts and has a number of other useful properties such as lower-semicontinuity. The framework allows general, possibly non-convex data terms. Experimental results are superior to those obtained without special care about wrapping interval end points. Moreover, we propose an equivalent formulation of the total cyclic variation which can be minimized with the same time and memory efficiency as the standard total variation.
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