Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing write by Jean-Francois Giovannelli. This book was released on 2015-02-16. Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing available in PDF, EPUB and Kindle. The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has since recognized that these matters are more interesting and they have become the subject of much greater enthusiasm. From the application field’s point of view, a significant part of the book is devoted to conventional subjects in the field of inversion: biological and medical imaging, astronomy, non-destructive evaluation, processing of video sequences, target tracking, sensor networks and digital communications. The variety of chapters is also clear, when we examine the acquisition modalities at stake: conventional modalities, such as tomography and NMR, visible or infrared optical imaging, or more recent modalities such as atomic force imaging and polarized light imaging.
Bayesian Methods for Inverse Problems in Signal and Image Processing
Bayesian Methods for Inverse Problems in Signal and Image Processing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bayesian Methods for Inverse Problems in Signal and Image Processing write by Yosra Marnissi. This book was released on 2017. Bayesian Methods for Inverse Problems in Signal and Image Processing available in PDF, EPUB and Kindle. Bayesian approaches are widely used in signal processing applications. In order to derive plausible estimates of original parameters from their distorted observations, they rely on the posterior distribution that incorporates prior knowledge about the unknown parameters as well as informations about the observations. The posterior mean estimator is one of the most commonly used inference rule. However, as the exact posterior distribution is very often intractable, one has to resort to some Bayesian approximation tools to approximate it. In this work, we are mainly interested in two particular Bayesian methods, namely Markov Chain Monte Carlo (MCMC) sampling algorithms and Variational Bayes approximations (VBA).This thesis is made of two parts. The first one is dedicated to sampling algorithms. First, a special attention is devoted to the improvement of MCMC methods based on the discretization of the Langevin diffusion. We propose a novel method for tuning the directional component of such algorithms using a Majorization-Minimization strategy with guaranteed convergence properties.Experimental results on the restoration of a sparse signal confirm the performance of this new approach compared with the standard Langevin sampler. Second, a new sampling algorithm based on a Data Augmentation strategy, is proposed to improve the convergence speed and the mixing properties of standard MCMC sampling algorithms. Our methodological contributions are validated on various applications in image processing showing the great potentiality of the proposed method to manage problems with heterogeneous correlations between the signal coefficients.In the second part, we propose to resort to VBA techniques to build a fast estimation algorithm for restoring signals corrupted with non-Gaussian noise. In order to circumvent the difficulties raised by the intricate form of the true posterior distribution, a majorization technique is employed to approximate either the data fidelity term or the prior density. Thanks to its flexibility, the proposed approach can be applied to a broad range of data fidelity terms allowing us to estimate the target signal jointly with the associated regularization parameter. Illustration of this approach through examples of image deconvolution in the presence of mixed Poisson-Gaussian noise, show the good performance of the proposed algorithm compared with state of the art supervised methods.
Bayesian Approach to Inverse Problems
Bayesian Approach to Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bayesian Approach to Inverse Problems write by Jérôme Idier. This book was released on 2013-03-01. Bayesian Approach to Inverse Problems available in PDF, EPUB and Kindle. 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.
Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing
Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing write by Jean-Francois Giovannelli. This book was released on 2015-02-02. Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing available in PDF, EPUB and Kindle. The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has since recognized that these matters are more interesting and they have become the subject of much greater enthusiasm. From the application field’s point of view, a significant part of the book is devoted to conventional subjects in the field of inversion: biological and medical imaging, astronomy, non-destructive evaluation, processing of video sequences, target tracking, sensor networks and digital communications. The variety of chapters is also clear, when we examine the acquisition modalities at stake: conventional modalities, such as tomography and NMR, visible or infrared optical imaging, or more recent modalities such as atomic force imaging and polarized light imaging.
Bayesian Inference for Inverse Problems
Bayesian Inference for Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bayesian Inference for Inverse Problems write by Ali Mohammad-Djafari. This book was released on 1998. Bayesian Inference for Inverse Problems available in PDF, EPUB and Kindle.
