# Coupled Reconstruction of 2D Blood Flow and Vessel Geometry from Noisy Images via Physics-Informed Neural Networks and Quasi-Conformal Mapping

arXiv: https://arxiv.org/abs/2508.11216 · HTML: https://mlsanity.com/paper/2508.11216/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 6 of 6)

- [Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization](https://mlsanity.com/paper/2103.16768/) (2021)
- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis](https://mlsanity.com/paper/2310.02641/) (2023)
- [Joint reconstruction and segmentation of noisy velocity images as an inverse Navier-Stokes problem](https://mlsanity.com/paper/2207.01368/) (2022)
- [Bayesian inverse Navier-Stokes problems: joint flow field reconstruction and parameter learning](https://mlsanity.com/paper/2406.18464/) (2024)
- [On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising](https://mlsanity.com/paper/1510.02923/) (2015)

## Abstract (arXiv)

Blood flow imaging provides important information for hemodynamic behavior within the vascular system and plays an essential role in medical diagnosis and treatment planning. However, obtaining high-quality flow images remains a significant challenge. In this work, we address the problem of denoising flow images that may suffer from artifacts due to short acquisition times or device-induced errors. We formulate this task as an optimization problem, where the objective is to minimize the discrepancy between the modeled velocity field, constrained to satisfy the Navier-Stokes equations, and the observed noisy velocity data. To solve this problem, we decompose it into two subproblems: a fluid subproblem and a geometry subproblem. The fluid subproblem leverages a Physics-Informed Neural Network to reconstruct the velocity field from noisy observations, assuming a fixed domain. The geometry subproblem aims to infer the underlying flow region by optimizing a quasi-conformal mapping that deforms a reference domain. These two subproblems are solved in an alternating Gauss-Seidel fashion, iteratively refining both the velocity field and the domain. Upon convergence, the framework yields a high-quality reconstruction of the flow image. We validate the proposed method through experiments on synthetic flow data in a converging channel geometry under varying levels of Gaussian noise, and on real-like flow data in an aortic geometry with signal-dependent noise. The results demonstrate the effectiveness and robustness of the approach. Additionally, ablation studies are conducted to assess the influence of key hyperparameters.