Related papers: PDE-constrained optimization in medical image anal…
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…
Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…
PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…
Recently, diagnosis, therapy and monitoring of human diseases involve a variety of imaging modalities, such as magnetic resonance imaging(MRI), computed tomography(CT), Ultrasound(US) and Positron-emission tomography(PET) as well as a…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
Objective: Deformable image registration is a fundamental problem in medical image analysis, with applications such as longitudinal studies, population modeling, and atlas based image segmentation. Registration is often phrased as an…
Image registration plays an important role in medical image analysis. Conventional optimization based methods provide an accurate estimation due to the iterative process at the cost of expensive computation. Deep learning methods such as…
Medical Informatics and the application of modern signal processing in the assistance of the diagnostic process in medical imaging is one of the more recent and active research areas today. This thesis addresses a variety of issues related…
We present a multi-species partial differential equation (PDE) model for tumor growth and a an algorithm for calibrating the model from magnetic resonance imaging (MRI) scans. The model is designed for glioblastoma (GBM) brain tumors. The…
The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model…
We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through…
Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the…
Image registration is a fundamental medical image analysis task. Ideally, registration should focus on aligning semantically corresponding voxels, i.e., the same anatomical locations. However, existing methods often optimize similarity…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
Deformable image registration is a fundamental problem in the field of medical image analysis. During the last years, we have witnessed the advent of deep learning-based image registration methods which achieve state-of-the-art performance,…
Deformable registration of magnetic resonance images between patients with brain tumors and healthy subjects has been an important tool to specify tumor geometry through location alignment and facilitate pathological analysis. Since tumor…
Inverse problems are crucial for many applications in science, engineering and medicine that involve data assimilation, design, and imaging. Their solution infers the parameters or latent states of a complex system from noisy data and…
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
Medical image registration seeks to find an optimal spatial transformation that best aligns the underlying anatomical structures. These problems usually require the optimization of a similarity metric. Swarm Intelligence techniques are very…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…