Total Tomography

W ritten by and primarily for experts in the field of discrete to-mography (DT) and its applications, students, programmers, scientists, and engineers alike will find a wealth of well-presented theoretical and practical material in Advances in Discrete To-mography and Its Applications. Gabor T. Herman is a prolific author and pioneer in the computerized tomography (CT) field and is recognized worldwide as an authority on medical image reconstruction techniques. Attila Kuba's vast contributions to the DT field include publishing original manuscripts, producing software packages—Idicon for the efficient conversion of Interfile images and the Discrete Reconstruction Techniques toolkit for DT recon-struction—and chairing or organizing several summer school programs and conferences on DT, medical imaging, and signal processing. The current volume is part of Springer's Applied and Numerical Harmonic Analysis series, which seeks to highlight " the intricate and fundamental relationship between harmonic analysis and fields such as signal processing, partial differential equations , and image processing. " DT is the process of reconstructing an image from a set of projections (that is, a set of measurements along a given direction) of that image. A cursory view of the extensive bibliography shows that DT has substantive applications in areas ranging from industry (detection of coking on turbine blades) to medicine (3D reconstruction of cardiac vessel structures). Despite the sometimes dense mathematical content, the selected contributions are clear and complete. The editors wisely break the text into three sections, all covered with equal depth and breadth—foundational material, reconstruction algorithms, and applications. The text's exercises, exhaustive solutions, and expert remarks also make it a suitable reference for a special topics class. Guided by well-crafted chapter summaries, motivated students and professionals will find the text a welcome handbook and resource. Although the text covers familiar concepts such as connectedness, con-vexity, and directedness, its claim to be a self-contained volume is stretched at times. In particular, some readers might view the treatment on finding components somewhat brief. More often—as the inclusion of a proof for the correctness and complexity measures illustrates—the coverage goes beyond the mundane. The text discusses important constructs such as decomposability at depth and gives reconstruction algorithm examples using multiple sets that have the same horizontal and vertical projections. The pertinent comments included by the author-experts add to the text's quality and readability and help underscore DT's applied nature. Care is also taken to point to relevant historical reviews and seminal articles in which …