{"ID":2881799,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.11216","arxiv_id":"2508.11216","title":"Coupled Reconstruction of 2D Blood Flow and Vessel Geometry from Noisy Images via Physics-Informed Neural Networks and Quasi-Conformal Mapping","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.","short_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 m...","url_abs":"https://arxiv.org/abs/2508.11216","url_pdf":"https://arxiv.org/pdf/2508.11216v2","authors":"[\"Han Zhang\",\"Xue-Cheng Tai\",\"Jean-Michel Morel\",\"Raymond H. Chan\"]","published":"2025-08-15T04:49:07Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.CV\"]","methods":"[]","has_code":false}