Related papers: A Comparative Study of MAP and LMMSE Estimators fo…
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the…
Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix H so as to minimize the mean square error (MSE) when estimating x from y. This problem has important…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred…
Modern instance-based model-agnostic explanation methods (LIME, SHAP, L2X) are of great use in data-heavy industries for model diagnostics, and for end-user explanations. These methods generally return either a weighting or subset of input…
Precoding design based on weighted sum-rate (WSR) maximization is a fundamental problem in downlink multi-user multiple-input multiple-output (MU-MIMO) systems. While the weighted minimum mean-square error (WMMSE) algorithm is a standard…
In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional…
Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming…
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…
Hyperspectral and multispectral images fusion aims at integrating a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to construct a high-resolution hyperspectral image (HR-HSI). It is generally…
The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…
We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…
In this paper, robust transceiver design based on minimum-mean-square-error (MMSE) criterion for dual-hop amplify-and-forward MIMO relay systems is investigated. The channel estimation errors are modeled as Gaussian random variables, and…
We consider the multichannel blind deconvolution problem where we observe the output of multiple channels that are all excited with the same unknown input. From these observations, we wish to estimate the impulse responses of each of the…
Despite the simplicity and intuitive interpretation of Minimum Mean Squared Error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of…
This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of…
Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…
Matrix ellipsoids provide a standard framework for representing bounded uncertainties in data-driven control. Since noise models for sequential observations are naturally represented as the Minkowski sum of multiple matrix ellipsoids,…
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…