相关论文: Inverse Problem Regularization for 3D Multi-Specie…

We propose a mathematical model for the growth and treatment dynamics of Undifferentiated Pleomorphic Sarcoma (UPS) based on a system of nonlinear differential equations. The model integrates Gompertz-type tumor growth with surface-area…

Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…

This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since…

Providing effective treatment and making informed clinical decisions are essential goals of modern medicine and clinical care. We are interested in simulating disease dynamics for clinical decision-making, leveraging recent advances in…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained…

The ability to estimate how a tumor might evolve in the future could have tremendous clinical benefits, from improved treatment decisions to better dose distribution in radiation therapy. Recent work has approached the glioma growth…

A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…

Gliomas are the most common malignant brain tumors in adults and are among the most lethal. Despite aggressive treatment, the median survival rate is less than 15 months. Accurate multiparametric MRI (mpMRI) tumor segmentation is critical…

We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to immune cell infiltrations. In this work, we normalize the…

Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free…

Accurate segmentation of brain tumors plays a key role in the diagnosis and treatment of brain tumor diseases. It serves as a critical technology for quantifying tumors and extracting their features. With the increasing application of deep…

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…

Registration of brain scans with pathologies is difficult, yet important research area. The importance of this task motivated researchers to organize the BraTS-Reg challenge, jointly with IEEE ISBI 2022 and MICCAI 2022 conferences. The…

Glioma is one of the most common and aggressive types of primary brain tumors. The accurate segmentation of subcortical brain structures is crucial to the study of gliomas in that it helps the monitoring of the progression of gliomas and…

A brain tumour is a mass or cluster of abnormal cells in the brain, which has the possibility of becoming life-threatening because of its ability to invade neighbouring tissues and also form metastases. An accurate diagnosis is essential…