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

TL;DR

This paper introduces a novel method combining physics-informed neural networks and quasi-conformal mapping to denoise and reconstruct 2D blood flow and vessel geometry from noisy images, improving medical diagnostics.

Contribution

It proposes an iterative framework that jointly reconstructs flow fields and vessel geometry from noisy data using physics constraints and geometric optimization.

Findings

Effective denoising of synthetic flow data with Gaussian noise

Robust reconstruction of flow and geometry in real-like aortic data

Ablation studies highlight key hyperparameters' impact

Abstract

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.