Ml Parameter Estimation For Markov Random Fields With Applications To Bayesian Tomography
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ML Parameter Estimation for Markov Random Fields, with Applications to Bayesian Tomography
Abstract: "Markov random fields (MRF) have proven useful for modeling the a priori information in Bayesian tomographic reconstruction problems. However, optimal parameter estimation of the MRF model remains a difficult problem due to the intractable nature of the partition function. In this report, we propose a fast parameter estimation scheme to obtain optimal estimates of the free parameters associated with a general MRF model formulation. In particular, for the generalized Gaussian MRF (GGMRF) case, we show that the ML estimate of the temperature T has a simple closed form solution. We present an efficient scheme for the ML estimate of the shape parameter p by an off-line numerical computation of the log of the partition function. We show that this approach can be extended to compute the parameters associated with a general MRF model. In the context of tomographic reconstruction, the difficulty of the ML estimation problem is compounded by the fact that the parameters depend on the unknown image. The EM algorithm is used to solve this problem. We derive fast simulation techniques for efficient computation of the expectation step. We also propose a method to extrapolate the estimates when the simulations are terminated prematurely prior to convergence. Experimental results for the emission and transmission case show that the proposed methods result in substantial savings in computation and superior quality images."
Bayesian Approach to Inverse Problems
Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.
Signal and Image Processing for Remote Sensing
Most data from satellites are in image form, thus most books in the remote sensing field deal exclusively with image processing. However, signal processing can contribute significantly in extracting information from the remotely sensed waveforms or time series data. Pioneering the combination of the two processes, Signal and Image Processing for Remote Sensing provides a balance between the role of signal processing and image processing in remote sensing. Featuring contributions from worldwide experts, this book emphasizes mathematical approaches. Divided into two parts, Part I examines signal processing for remote sensing and Part II explores image processing. Not limited to the problems with data from satellite sensors, the book considers other sensors which acquire data remotely, including signals and images from infrasound, seismic, microwave, and satellite sensors. It covers a broader scope of issues in remote sensing information processing than other books in this area. With rapid technological advances, the mathematical techniques provided will far outlast the sensor, software and hardware technologies. Focusing on methodologies of signal processing and image processing in remote sensing, this book discusses unique techniques for dealing with remote sensing problems.