相关论文: On the identification of piecewise constant coeffi…

Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Image segmentation is a fundamental research topic in image processing and computer vision. In the last decades, researchers developed a large number of segmentation algorithms for various applications. Amongst these algorithms, the…

In this article, we consider elliptic diffusion problems on random domains with non-smooth diffusion coefficients. We start by illustrating the problems that arise from a non-smooth diffusion coefficient by recapitulating the corresponding…

We present an inference-time diffusion sampling method to perform multi-view consistent image editing using pre-trained 2D image editing models. These models can independently produce high-quality edits for each image in a set of multi-view…

The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard…

An active learning algorithm for the classification of high-dimensional images is proposed in which spatially-regularized nonlinear diffusion geometry is used to characterize cluster cores. The proposed method samples from estimated cluster…

Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…

In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed…

Limited data is a common problem in remote sensing due to the high cost of obtaining annotated samples. In the few-shot segmentation task, models are typically trained on base classes with abundant annotations and later adapted to novel…

Optical Coherence Tomography(OCT) is a non-invasive technique capturing cross-sectional area of the retina in micro-meter resolutions. It has been widely used as a auxiliary imaging reference to detect eye-related pathology and predict…

Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric…

Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…

This paper presents a novel method for the reconstruction of high-resolution temporal images in dynamic tomographic imaging, particularly for discrete objects with smooth boundaries that vary over time. Addressing the challenge of limited…

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

In hydrology, the degradation coefficient is one of the key parameters to describe the water quality change and to determine the water carrying capacity. This paper is devoted to identify the degradation coefficient in an anomalous…

Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse problem. Models with total variational (TV) regularization…

This work presents an overview of several nonlinear reduction strategies for data compression from various research fields, and a comparison of their performance when applied to problems characterized by diffusion and/or advection terms. We…