相关论文: Bayes-optimal inverse halftoning and statistical m…

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…

We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…

This paper presents an innovative approach to computational acoustic imaging of biperiodic surfaces, exploiting the capabilities of an acoustic superlens to overcome the diffraction limit. We address the challenge of imaging physical…

We consider the statistical inverse problem of recovering an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the…

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and…

This work considers sequential edge-promoting Bayesian experimental design for (discretized) linear inverse problems, exemplified by X-ray tomography. The process of computing a total variation type reconstruction of the absorption inside…

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…

The Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, for problems with non-unique solutions, the classical estimators such as the maximum a…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

Local algorithms are common tools for estimating intrinsic volumes from black-and-white digital images. However, these algorithms are typically biased in the design based setting, even when the resolution tends to infinity. Moreover, images…

When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…

We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…

We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In…

In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an l1-regularized least squares cost function. This result can also be derived by employing a…

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method…

Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…

This paper tackles the problem of image deconvolution with joint estimation of PSF parameters and hyperparameters. Within a Bayesian framework, the solution is inferred via a global a posteriori law for unknown parameters and object. The…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…