Tikhonov Regularization of Circle-Valued Signals

TL;DR

This paper introduces a convex relaxation approach using semidefinite programming to effectively smooth and interpolate circle-valued signals on arbitrary graphs, addressing the challenges of processing cyclic data.

Contribution

It presents a novel convex relaxation model for Tikhonov regularization of circle-valued signals and an efficient algorithm for solving it.

Findings

The relaxation is convex and solvable via semidefinite programming.

The proposed method effectively smooths and interpolates cyclic signals.

The algorithm demonstrates computational efficiency on various graph structures.

Abstract

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.