Related papers: An Additive Approximation to Multiplicative Noise

In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…

In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the…

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the…

How should one combine noisy information from diverse sources to make an inference about an objective ground truth? This frequently recurring, normative question lies at the core of statistics, machine learning, policy-making, and everyday…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…

Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…

The Laplace approximation is sometimes not sufficiently accurate for smoothing parameter estimation in generalized additive mixed models. A novel estimation strategy is proposed that solves this problem and leads to estimates exhibiting the…

In this article, we consider two different statistical models. First, we focus on the estimation of the jump intensity of a compound Poisson process in the presence of unknown noise. This problem combines both the deconvolution problem and…

In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…

Crowdsourcing has emerged as an effective means for performing a number of machine learning tasks such as annotation and labelling of images and other data sets. In most early settings of crowdsourcing, the task involved classification,…

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

Imaging is a standard example of an inverse problem, where the task of reconstructing a ground truth from a noisy measurement is ill-posed. Recent state-of-the-art approaches for imaging use deep learning, spearheaded by unrolled and…

Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses.…

Multiplicative noise, also known as speckle or pepper noise, commonly affects images produced by synthetic aperture radar (SAR), lasers, or optical lenses. Unlike additive noise, which typically arises from thermal processes or external…

We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…

We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular…