Tikhonov Regularization of Sphere-Valued Signals

TL;DR

This paper introduces a Tikhonov regularization approach for smoothing and interpolating signals on the sphere defined over arbitrary graphs, using a convex relaxation as a semidefinite program for efficient computation.

Contribution

It proposes a novel convex relaxation of a nonconvex sphere-valued signal regularization problem, enabling practical and efficient solutions.

Findings

Convex relaxation effectively approximates the original problem.

Semidefinite programming provides a practical solution method.

Method applicable to signals on arbitrary graphs.

Abstract

It is common to have to process signals, whose values are points on the 3-D sphere. We consider a Tikhonov-type regularization model to smoothen or interpolate sphere-valued signals defined on arbitrary graphs. We propose a convex relaxation of this nonconvex problem as a semidefinite program, which is easy to solve numerically and is efficient in practice.