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

Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an…

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…

All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum.…

In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is two-fold. Firstly, we formulate the restoration…

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…

Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…

Color artifacts of demosaicked images are often found at contours due to interpolation across edges and cross-channel aliasing. To tackle this problem, we propose a novel demosaicking method to reliably reconstruct color channels of a Bayer…

We consider the statistical nonlinear inverse problem of recovering the absorption term $f>0$ in the heat equation $$ \partial_tu-\frac{1}{2}\Delta u+fu=0 \quad \text{on $\mathcal{O}\times(0,\textbf{T})$}\quad u = g \quad \text{on…

We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

Signal inpainting is the task of restoring degraded or missing samples in a signal. In this paper we address signal inpainting when Fourier magnitudes are observed. We propose a mathematical formulation of the problem that highlights its…

We study the well-known problem of estimating a sparse $n$-dimensional unknown mean vector $\theta = (\theta_1, ..., \theta_n)$ with entries corrupted by Gaussian white noise. In the Bayesian framework, continuous shrinkage priors which can…

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…

We address the problem of image color quantization using a Maximum Entropy based approach. Focusing on pixel mapping we argue that adding thermal noise to the system yields better visual impressions than that obtained from a simple energy…

In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of…

Image quantization is used in several applications aiming in reducing the number of available colors in an image and therefore its size. De-quantization is the task of reversing the quantization effect and recovering the original…

We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…

Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…