Related papers: Diffusion tensor imaging with deterministic error …
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…
Recent advancements in text-to-image models, such as Stable Diffusion, show significant demographic biases. Existing de-biasing techniques rely heavily on additional training, which imposes high computational costs and risks of compromising…
Knowledge of the noise distribution in diffusion MRI is the centerpiece to quantify uncertainties arising from the acquisition process. Accurate estimation beyond textbook distributions often requires information about the acquisition…
In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability…
The recent development of diffusion models has led to significant progress in solving inverse problems by leveraging these models as powerful generative priors. However, challenges persist due to the ill-posed nature of such problems, often…
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem related to thermoacoustic tomography, a nonlinear inverse…
We develop a principled framework for analyzing and designing noise schedules in diffusion models. We show that one can recast this design problem as an optimal control problem, whose state is the Fisher information of the diffusion process…
In this paper, by means of a standard model problem, we devise an approach to computing approximate dual bounds for use in global optimization of coefficient identification in partial differential equations (PDEs) by, e.g., (spatial)…
Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…
Time series anomaly detection (TSAD) has been an important area of research for decades, with reconstruction-based methods, mostly based on generative models, gaining popularity and demonstrating success. Diffusion models have recently…
Diffusion models have recently been shown to excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. A common framework uses task-agnostic unconditional models that are later…
In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent…
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…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Standard machine learning is unable to accommodate inputs which do not belong to the training distribution. The resulting models often give rise to confident incorrect predictions which may lead to devastating consequences. This problem is…
We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we…
Medical image segmentation often involves inherent uncertainty due to variations in expert annotations. Capturing this uncertainty is an important goal and previous works have used various generative image models for the purpose of…
Recent work has shown that diffusion models trained with the denoising score matching (DSM) objective often violate the Fokker--Planck (FP) equation that governs the evolution of the true data density. Directly penalizing these deviations…