A variational model for wrapped phase denoising

TL;DR

This paper presents a novel variational model for denoising wrapped phase images that preserves phase discontinuities and enforces trigonometric identities, with proven existence, uniqueness, and a convergent solution method.

Contribution

It introduces a total variation based model that improves phase denoising by maintaining discontinuities and enforcing trigonometric identities, with theoretical guarantees and an efficient solution method.

Findings

Model preserves phase discontinuities effectively.

Theoretical proof of existence and uniqueness of solutions.

Experimental validation on synthetic and real data.

Abstract

In this paper, we introduce a total variation based variational model for denoising wrapped phase images. Our model improves on former methods by preserving discontinuities of the phase map and enforcing the fundamental Pythagorean trigonometric identity between the real and imaginary parts of the phase map enhancing the quality of the restored phase. The existence and uniqueness of the solution of our model is proven using standard methods. Further, we provide a fast fixed point method for finding the numerical solution and prove its convergence. Experiments on both synthetic and real patterns verify our findings.