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Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…

Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in…

Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…

Inverse scattering problems are critical in electromagnetic imaging and medical diagnostics but are challenged by their nonlinearity and diverse measurement scenarios. This paper proposes a physics-informed deep contrast source inversion…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

Recently, the explicit constraint force method (ECFM) was introduced as a principled approach to solution reconstruction in the presence of missing physics. In solution reconstruction, parameters of a physical model are estimated from…

We study an inverse problem for Light Sheet Fluorescence Microscopy (LSFM), where the density of fluorescent molecules needs to be reconstructed. Our first step is to present a mathematical model to describe the measurements obtained by an…

Self-supervised multi-frame methods have currently achieved promising results in depth estimation. However, these methods often suffer from mismatch problems due to the moving objects, which break the static assumption. Additionally,…

Optical spectroscopy is indispensable for research and development in nanoscience and nanotechnology, microelectronics, energy, and advanced manufacturing. Advanced optical spectroscopy tools often require both specifically designed…

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…

Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental…

Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…

Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…

We present a unifying framework to solve several computer vision problems with event cameras: motion, depth and optical flow estimation. The main idea of our framework is to find the point trajectories on the image plane that are best…

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

In this study, we investigate the inverse source problem arising in bioluminescence tomography, the objective of which is to reconstruct both the support and the intensity of an internal light source from boundary measurements governed by…