This attractively titled book deals with the process of creating images using raw noisy data from unknown sources such as a black hole, for example. This book arose out of the notes used for a graduate-level course on this topic for over two decades. Using the standard Bayesian framework, the author formulates this image reconstruction problem as a classical inverse problem. Within this framework, the problems in this class are divided along several characteristic dimensions: one versus two physical dimensions, causal versus noncausal analysis, continuous versus discrete time, and Gaussian versus non-Gaussian frameworks. The book is organized to reveal the beauty and the challenges that arise along these characteristic dimensions. The book is divided into a total of 17 short chapters along with four appendices.
A short but succinct introduction to computational imaging is provided in the opening chapter. Chapters 2 to 4 follow with an overview of basic probabilistic tools and 1D and 2D causal and non-causal Gaussian (Markov random field) models. The next three chapters (5 through 7) describe basic tools and algorithms for MAP estimation. Chapters 8 to 10 cover results from constrained optimization algorithms needed to pursue the rest of the book. Model parameter estimation is discussed in detail in chapter 11. The next three chapters (12 to 15) provide an excellent introduction to the key ideas related to the EM algorithm, Markov chains and hidden Markov chains (HMM), and stochastic simulation covering various sampling techniques. The last two chapters (16 and 17) describe the Bayesian segmentation and Poisson data models. The four appendices supplement the developments in the main body of the book. Each chapter contains a good set of exercise problems, and there is a list of nearly 100 relevant references to the literature. The index is useful for navigating the material.
This excellent textbook could be used in graduate-level courses on this topic for many years to come.
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