Related papers: Solving Inverse Problems with a Flow-based Noise M…
Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving…
Image denoisers have been shown to be powerful priors for solving inverse problems in imaging. In this work, we introduce a generalization of these methods that allows any image restoration network to be used as an implicit prior. The…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
We propose a general framework for solving inverse problems in the presence of noise that requires no signal prior, no noise estimate, and no clean training data. We only require that the forward model be available and that the noise be…
We develop a \emph{flow-matching framework} for transporting probability measures under control-affine dynamics and for steering systems to points or target sets. Starting from the continuity equation associated with the control affine…
Image reconstruction from computed tomography (CT) measurement is a challenging statistical inverse problem since a high-dimensional conditional distribution needs to be estimated. Based on training data obtained from high-quality…
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…
Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates…
Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
Inverse rendering, the process of inferring scene properties from images, is a challenging inverse problem. The task is ill-posed, as many different scene configurations can give rise to the same image. Most existing solutions incorporate…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is…
Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows.…
Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…
Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…
Proper regularization is crucial in inverse problems to achieve high-quality reconstruction, even with an ill-conditioned measurement system. This is particularly true for three-dimensional photoacoustic tomography, which is computationally…