相关论文: PDE-constrained optimization in medical image anal…
Despite the recent success of deep learning methods at achieving new state-of-the-art accuracy for medical image segmentation, some major limitations are still restricting their deployment into clinics. One major limitation of deep…
An important topic in medical research is the process of improving the images obtained from medical devices. As a consequence, there is also a need to improve medical image resolution and analysis. Another issue in this field is the large…
In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total…
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…
Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale…
We are interested in the optimization of convex domains under a PDE constraint. Due to the difficulties of approximating convex domains in $\mathbb{R}^3$, the restriction to rotationally symmetric domains is used to reduce shape…
Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…
Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging,…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
To accelerate MRI, the field of compressed sensing is traditionally concerned with optimizing the image quality after a partial undersampling of the measurable $\textit{k}$-space. In our work, we propose to change the focus from the quality…
In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which…
The medical imaging literature has witnessed remarkable progress in high-performing segmentation models based on convolutional neural networks. Despite the new performance highs, the recent advanced segmentation models still require large,…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
The task of medical image segmentation presents unique challenges, necessitating both localized and holistic semantic understanding to accurately delineate areas of interest, such as critical tissues or aberrant features. This complexity is…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of…
The correlation of optical measurements with a correct pathology label is often hampered by imprecise registration caused by deformations in histology images. This study explores an automated multi-modal image registration technique…
We propose a novel approach to image segmentation based on combining implicit spline representations with deep convolutional neural networks. This is done by predicting the control points of a bivariate spline function whose zero-set…
We consider some iterative methods for finding the best interpolation data in the images compression with noise. The interpolation data consists of the set of pixels and their grey/color values. The aim in the iterative approach is to allow…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…