相关论文: Optimization of the shape (and topology) of the in…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

Fluorescence recovery after photobleaching (FRAP) measurements offer an important tool for analyzing diffusion and binding processes. Confocal scanning laser microscopes that are used in FRAP experiments bleach regions with a radially…

The identification of the interface of an inclusion in a diffusion process is considered. This task is viewed as a parameter identification problem in which the parameter space bears the structure of a shape manifold. A corresponding…

Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work…

Designing topological materials with specific topological indices is a complex inverse problem, traditionally tackled through manual, intuition-driven methods that are neither scalable nor efficient for exploring the vast space of possible…

Understanding transcription factor dynamics is crucial for unraveling the regulatory mechanisms of gene expression that underpin cellular function and development. Measurements of transcription factor subcellular movements are essential for…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…

Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused…

We describe how a single-particle tracking experiment should be designed in order for its recorded trajectories to contain the most information about a tracked particle's diffusion coefficient. The precision of estimators for the diffusion…

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…

The transport and localization of RNA molecules, crucial for cellular function and development, involve a combination of diffusion and active transport mechanisms. Here, we are motivated by understanding the dynamics of RNA in Xenopus…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

Diffusion models are widely used for generative tasks across domains. Given a pre-trained diffusion model, it is often desirable to fine-tune it further either to correct for errors in learning or to align with downstream applications.…

In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…

Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on…

Previously we considered the effect of experimental parameters on optimized transmission through opaque media using spatial light modulator (SLM)-based wavefront shaping. In this study we consider the opposite geometry, in which we optimize…

Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…