Related papers: Diffusion tensor imaging with deterministic error …

We study two-layer neural networks whose domain and range are Banach spaces with separable preduals. In addition, we assume that the image space is equipped with a partial order, i.e. it is a Riesz space. As the nonlinearity we choose the…

Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…

In this paper we investigate the non-linear and ill-posed inverse problem of simultaneously identifying the conductivity and the reaction in diffuse optical tomography with noisy measurement data available on an accessible part of the…

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are…

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…

Recent research has shown that text-to-image diffusion models are capable of generating high-quality images guided by text prompts. But can they be used to generate or approximate real-world images from the seed noise? This is known as the…

Atmospheric Turbulence (AT) correction is a challenging restoration task as it consists of two distortions: geometric distortion and spatially variant blur. Diffusion models have shown impressive accomplishments in photo-realistic image…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited…

We study Talenti's type symmetrization properties for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal…

The statistical linearization method known in nonlinear mechanics and random vibrations theory has been applied to stochastically quantized fields in finite temperature. It has been shown that even in its simplest form the method yields…

We consider the identification of scattering and absorption rates in the stationary radiative transfer equation. For a stable solution of this parameter identification problem, we consider Tikhonov regularization within Banach spaces. A…

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the…

Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

We take advantage of recent and new results on optimal quantization theory to improve the quadratic optimal quantization error bounds for backward stochastic differential equations (BSDE) and nonlinear filtering problems. For both problems,…

This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are…

In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with…

Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…