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

arXiv: https://arxiv.org/abs/2109.05496 · HTML: https://mlsanity.com/paper/2109.05496/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 48 references that are in the map.
- First posted on arXiv 12 Sep 2021.

## Builds on (most cited first, 2 of 2)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Resolution analysis in a lens-free on-chip digital holographic microscope](https://mlsanity.com/paper/1906.06231/) (2019)

## Built on by (most cited first, 1 of 1)

- [Position-Blind Ptychography: Viability of image reconstruction via data-driven variational inference](https://mlsanity.com/paper/2509.25269/) (2025)

## Abstract (arXiv)

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.