A Complex Constrained Total Variation Image Denoising Algorithm with Application to Phase Retrieval

TL;DR

This paper develops a novel complex-valued total variation denoising algorithm using a dual approach, which improves phase retrieval and other complex image processing tasks by incorporating constraints and accelerating convergence.

Contribution

It introduces new complex TV definitions, an accelerated gradient projection algorithm, and a generalized framework for complex constrained optimization with TV regularizers.

Findings

Effective in phase retrieval applications

Speeds up convergence in complex image denoising

Validates the approach with simulated and optical experiments

Abstract

This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two types of complex TV in both isotropic and anisotropic forms. To solve the constrained denoising problem, we adopt a dual approach and derive an accelerated gradient projection algorithm. We further generalize the proposed denoising algorithm as a key building block of the proximal gradient scheme to solve a vast class of complex constrained optimization problems with TV regularizers. As an example, we apply the proposed algorithmic framework to phase retrieval. We combine the complex TV regularizer with the conventional projection-based method within the constraint complex TV model. Initial results from both simulated and optical experiments demonstrate the validity of the constrained TV model in extracting sparsity priors within complex-valued images, while also utilizing physically tractable constraints that help speed up convergence.