Statistical Image Processing and Multidimensional Modeling (Information Science and Statistics)

Images are all around us! The proliferation of low-cost, high-quality imaging devices has led to an explosion in acquired images. When these images are acquired from a microscope, telescope, satellite, or medical imaging device, there is a statistical image processing task: the inference of something--an artery, a road, a DNA marker, an oil spill--from imagery, possibly noisy, blurry, or incomplete. A great many textbooks have been written on image processing. However this book does not so much focus on images, per se, but rather on spatial data sets, with one or more measurements taken over a two or higher dimensional space, and to which standard image-processing algorithms may not apply. There are many important data analysis methods developed in this text for such statistical image problems. Examples abound throughout remote sensing (satellite data mapping, data assimilation, climate-change studies, land use), medical imaging (organ segmentation, anomaly detection), computer vision (image classification, segmentation), and other 2D/3D problems (biological imaging, porous media). The goal, then, of this text is to address methods for solving multidimensional statistical problems. The text strikes a balance between mathematics and theory on the one hand, versus applications and algorithms on the other, by deliberately developing the basic theory (Part I), the mathematical modeling (Part II), and the algorithmic and numerical methods (Part III) of solving a given problem. The particular emphases of the book include inverse problems, multidimensional modeling, random fields, and hierarchical methods. Paul Fieguth is a professor in Systems Design Engineering at the University of Waterloo in Ontario, Canada. He has longstanding research interests in statistical signal and image processing, hierarchical algorithms, data fusion, and the interdisciplinary applications of such methods, particularly to problems in medical imaging, remote sensing, and scientific imaging Front Matter....Pages i-xxii Introduction....Pages 1-10 Front Matter....Pages 11-11 Inverse Problems....Pages 13-55 Static Estimation and Sampling....Pages 57-84 Dynamic Estimation and Sampling....Pages 85-129 Front Matter....Pages 131-131 Multidimensional Modelling....Pages 133-177 Markov Random Fields....Pages 179-214 Hidden Markov Models....Pages 215-239 Changes of Basis....Pages 241-290 Front Matter....Pages 291-291 Linear Systems Estimation....Pages 293-324 Kalman Filtering and Domain Decomposition....Pages 325-353 Sampling and Monte Carlo Methods....Pages 355-380 Front Matter....Pages 381-381 Algebra....Pages 383-409 Statistics....Pages 411-421 Image Processing....Pages 423-432 Back Matter....Pages 433-454 Pt. 1: Inverse problems and estimation -- Pt. 2: Modelling of random fields -- Pt. 3: Methods and algorithms -- Pt. 4: Appendices