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.
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