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Reviewer: Vladik Ya. Kreinovich

Jain has written a surprisingly complete survey of various methods connected with image processing. This book can serve as both a textbook and a monograph, from which an interested reader who omits the first introductory chapters and known details can learn a lot about digital image processing. Chapter 1 gives a brief survey of the problems. Chapter 2 covers the main mathematical techniques, such as Fourier transform, necessary results from matrix theory, random processes, estimates, and information theory. Chapter 3 is devoted to image perception, from simple well-known color space models to complicated quantitative models that consider spatial and temporal effects. Chapter 4 discusses image sampling and quantization, including optimal sampling, the impact of quantization, and optimal reconstruction from sample images. More complicated digital image processing techniques are based on more complicated mathematics that is described in chapter 5, which covers discrete Fourier transforms and Karhunen-Loeve transforms, and chapter 6, on random fields, causal models, and so on. Chapter 7 uses all this mathematics to describe different methods of enhancing images, that is, sharpening edges, boundaries, and contrasts (including false color methods). Chapter 8 covers image filtering and restoration, including not only the usual statistical methods but also maximum entropy methods, speckle reconstruction, and superresolution methods (extrapolation of band-limited signals). Chapter 9 discusses image analysis and computer vision (edge detection, shape detection, texture, scenes, and learning classification algorithms). Chapter 10 covers tomography, including the Radon transform and purely algebraic methods for both two- and three-dimensional cases. Chapter 11 discusses image data compression. It describes various, mainly adaptive methods that allow one to store, say, a TV picture in less than 6 MHz. The text can be read by beginners because it includes all necessary mathematics (even matrices, Fourier transforms, and random processes). A good pedagogic detail is the use of several typical images throughout the book to show how they are distorted by noise, how they are filtered, and so forth. Of course a book cannot be overwhelming. For example, Jain does not mention methods (and ideas and results) connected with problems that are typical for astronomy, for example, in very long baseline interferometry. The book omits image reconstruction from Fourier transforms known in finitely many points whose distribution is irregular (dense in some places, but not everywhere—- they correspond to baseline projections of real experiments); the problems of reconstructing an image from the modulus of a Fourier transform when phases are completely unknown, or when phase errors are essentially greater than amplitude errors; three-dimensional image processing (radioholography); and methods connected with reconstructing images from few points (the CLEAN iterative method) or images about which we know that they are the sum of few Gaussians. Nevertheless, the book gives a brilliant introduction to the main techniques, thus allowing the reader to learn additional methods easily.