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Linear inverse problems $A \mu = \delta$ with Poisson noise and non-negative unknown $\mu \geq 0$ are ubiquitous in applications, for instance in Positron Emission Tomography (PET) in medical imaging. The associated maximum likelihood…

Optimization and Control · Mathematics 2020-02-24 Camille Pouchol , Olivier Verdier

For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…

Signal Processing · Electrical Eng. & Systems 2023-11-30 Carter Lyons , Raghu G. Raj , Margaret Cheney

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…

Information Theory · Computer Science 2017-02-14 Dmitry Batenkov , Yaniv Romano , Michael Elad

Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…

Graphics · Computer Science 2025-04-22 Yu Guo , Milos Hasan , Lingqi Yan , Shuang Zhao

Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework…

Machine Learning · Statistics 2020-11-18 Zaccharie Ramzi , Benjamin Remy , Francois Lanusse , Jean-Luc Starck , Philippe Ciuciu

The semantic segmentation task aims at dense classification at the pixel-wise level. Deep models exhibited progress in tackling this task. However, one remaining problem with these approaches is the loss of spatial precision, often produced…

Computer Vision and Pattern Recognition · Computer Science 2022-07-20 Darwin Saire , Adín Ramírez Rivera

This paper presents a novel Bayesian approach for hyperspectral image unmixing. The observed pixels are modeled by a linear combination of material signatures weighted by their corresponding abundances. A spike-and-slab abundance prior is…

Applications · Statistics 2022-05-04 Zeng Li , Yoann Altmann , Jie Chen , Stephen Mclaughlin , Susanto Rahardja

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

Machine Learning · Computer Science 2026-05-04 Saeed Mohseni-Sehdeh , Walid Saad , Kei Sakaguchi , Tao Yu

Maximum-a-posteriori (MAP) approaches are an effective framework for inverse problems with known forward operators, particularly when combined with expressive priors and careful parameter selection. In blind settings, however, their use…

Information Theory · Computer Science 2026-02-13 Nathan Buskulic , Luca Calatroni

The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…

Optimization and Control · Mathematics 2025-03-14 Ji Li , Chao Wang

This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a…

Computation · Statistics 2022-05-20 Hwanwoo Kim , Daniel Sanz-Alonso , Alexander Strang

Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…

Machine Learning · Computer Science 2025-07-17 Shiqi Liu , Yihua Tan , Yutong Bai , Alan Yuille

The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…

Machine Learning · Statistics 2018-06-08 Richard Y. Zhang , Salar Fattahi , Somayeh Sojoudi

A successful approach to image quality assessment involves comparing the structural information between a distorted and its reference image. However, extracting structural information that is perceptually important to our visual system is a…

Computer Vision and Pattern Recognition · Computer Science 2021-03-17 Tanaya Guha , Ehsan Nezhadarya , Rabab K Ward

There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…

Statistics Theory · Mathematics 2026-03-24 Rémi Gribonval , Mila Nikolova

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.…

Image and Video Processing · Electrical Eng. & Systems 2021-11-11 Bahjat Kawar , Gregory Vaksman , Michael Elad

There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the…

Numerical Analysis · Mathematics 2021-12-01 William Reese , Arvind K. Saibaba , Jonghyun Lee

The feature frame is a key idea of feature matching problem between two images. However, most of the traditional matching methods only simply employ the spatial location information (the coordinates), which ignores the shape and orientation…

Computer Vision and Pattern Recognition · Computer Science 2019-10-29 Liang Shen , Jiahua Zhu , Chongyi Fan , Xiaotao Huang , Tian Jin

We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…

Systems and Control · Computer Science 2016-06-16 Reza Arablouei

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…

Numerical Analysis · Mathematics 2017-04-27 Yong-Xia Hao , Chong-Jun Li , Ren-Hong Wang