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Diffusion models have shown impressive performance for image generation, often times outperforming other generative models. Since their introduction, researchers have extended the powerful noise-to-image denoising pipeline to discriminative…

Image and Video Processing · Electrical Eng. & Systems 2023-12-21 Fahim Ahmed Zaman , Mathews Jacob , Amanda Chang , Kan Liu , Milan Sonka , Xiaodong Wu

We introduce multi-scale energy models to learn the prior distribution of images, which can be used in inverse problems to derive the Maximum A Posteriori (MAP) estimate and to sample from the posterior distribution. Compared to the…

Image and Video Processing · Electrical Eng. & Systems 2024-07-19 Jyothi Rikhab Chand , Mathews Jacob

The distortion-perception (D-P) tradeoff is a fundamental phenomenon of Bayesian inverse problems, which characterizes the inherent tension between distortion performance and perceptual quality. Enabling flexible traversal of the D-P…

Machine Learning · Computer Science 2026-05-29 Jiawei Zhang , Ziyuan Liu , Leon Yan , Zhenyu Xiao , Yuantao Gu

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…

Computer Vision and Pattern Recognition · Computer Science 2025-06-18 Giacomo Meanti , Thomas Ryckeboer , Michael Arbel , Julien Mairal

Accurate camera viewpoint estimation under sparse-view conditions remains challenging, particularly in two-view scenarios. Recent approaches leverage diffusion models such as Zero123 to synthesize novel views conditioned on relative…

Computer Vision and Pattern Recognition · Computer Science 2026-05-20 Yan-Ting Chen , Hao-Wei Chen , Tsu-Ching Hsiao , Chun-Yi Lee

We consider the inverse problem of recovering an unknown functional parameter $u$ in a separable Banach space, from a noisy observation $y$ of its image through a known possibly non-linear ill-posed map ${\mathcal G}$. The data $y$ is…

Statistics Theory · Mathematics 2018-03-14 Sergios Agapiou , Martin Burger , Masoumeh Dashti , Tapio Helin

This work studies the inverse problem of photoacoustic tomography (more precisely, the acoustic subproblem) as the identification of a space-dependent source parameter. The model consists of a wave equation involving a time-fractional…

Numerical Analysis · Mathematics 2025-04-29 Phuoc-Truong Huynh , Barbara Kaltenbacher

In the realm of medical imaging, inverse problems aim to infer high-quality images from incomplete, noisy measurements, with the objective of minimizing expenses and risks to patients in clinical settings. The Diffusion Models have recently…

Image and Video Processing · Electrical Eng. & Systems 2024-04-08 Hossein Askari , Fred Roosta , Hongfu Sun

We study zero-shot conditional sampling with pretrained diffusion models for linear inverse problems, including inpainting and super-resolution. In these problems, the observation determines only part of the unknown signal. The remaining…

Machine Learning · Computer Science 2026-05-08 Ahmad Aghapour , Erhan Bayraktar , Asaf Cohen

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…

Image and Video Processing · Electrical Eng. & Systems 2025-10-13 Darshan Thaker , Abhishek Goyal , René Vidal

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

Numerical Analysis · Mathematics 2015-06-05 Aleksandr Y. Aravkin , Tristan van Leeuwen

In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…

Methodology · Statistics 2020-03-17 Dimas Abreu Archanjo Dutra

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples…

Machine Learning · Computer Science 2025-08-19 Bingliang Zhang , Wenda Chu , Julius Berner , Chenlin Meng , Anima Anandkumar , Yang Song

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…

Machine Learning · Statistics 2024-09-16 Yaxuan Zhu , Zehao Dou , Haoxin Zheng , Yasi Zhang , Ying Nian Wu , Ruiqi Gao

Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to…

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…

Computer Vision and Pattern Recognition · Computer Science 2025-06-17 Zhen Wang , Hongyi Liu , Zhihui Wei

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes,…

Information Theory · Computer Science 2015-06-11 Emrah Bostan , Ulugbek S. Kamilov , Masih Nilchian , Michael Unser

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

Methodology · Statistics 2023-02-09 Xiao Liu , Kyongmin Yeo

Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However,…

Computer Vision and Pattern Recognition · Computer Science 2024-10-24 Jun Cheng , Shan Tan

We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…

Numerical Analysis · Mathematics 2019-05-22 Jeff Borggaard , Nathan E. Glatt-Holtz , Justin A. Krometis