相关论文: Regularization and Inverse Problems

To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are…

We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…

Wavelet functions allow the sparse and efficient representation of a signal at different scales. Recently the application of wavelets to the denoising of maps of cosmic microwave background (CMB) fluctuations has been proposed. The…

The Maximum Entropy Method (MEM) for the deconvolution of radio interferometry images is mathematically well based and presents a number of advantages over the usual CLEAN deconvolution, such as appreciably higher resolution. The…

An image restoration approach based on a Bayesian maximum entropy method (MEM) has been applied to a radiological image deconvolution problem, that of reduction of geometric blurring in magnification mammography. The aim of the work is to…

Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further…

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 paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

The Maximum Entropy Method (MEM) is a popular data analysis technique based on Bayesian inference, which has found various applications in the research literature. While the MEM itself is well-grounded in statistics, I argue that its…

Image deblurring is a notoriously challenging ill-posed inverse problem. In recent years, a wide variety of approaches have been proposed based upon regularization at the level of the image or on techniques from machine learning. We propose…

The main object of this paper is to show how we can use classical probabilistic methods such as Maximum Entropy (ME), maximum likelihood (ML) and/or Bayesian (BAYES) approaches to do microscopic and macroscopic data fusion. Actually ME can…

During the past few years, inverse problem formulations of ultrasound beamforming have attracted a growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a…

This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…