By Charles L. Epstein
On the center of each scientific imaging expertise is a cosmopolitan mathematical version of the dimension technique and an set of rules to reconstruct a picture from the measured facts. This e-book presents a company origin within the mathematical instruments used to version the measurements and derive the reconstruction algorithms utilized in so much imaging modalities in present use. within the approach, it additionally covers many vital analytic strategies and methods utilized in Fourier research, fundamental equations, sampling thought, and noise research.
this article makes use of X-ray computed tomography as a "pedagogical computing device" to demonstrate very important principles and contains huge discussions of heritage fabric making the extra complicated mathematical subject matters obtainable to readers with a much less formal mathematical schooling. The mathematical thoughts are illuminated with over two hundred illustrations and diverse workouts.
New to the second one version are a bankruptcy on magnetic resonance imaging (MRI), a revised part at the courting among the continuum and discrete Fourier transforms, a brand new part on Grangreat s formulation, a higher description of the gridding technique, and a brand new part on noise research in MRI.
viewers The ebook is acceptable for one- or two-semester classes on the complicated undergraduate or starting graduate point at the mathematical foundations of recent scientific imaging applied sciences. The textual content assumes an realizing of calculus, linear algebra, and simple mathematical research.
Contents Preface to the second one version; Preface; tips on how to Use This ebook; Notational Conventions; bankruptcy 1: Measurements and Modeling; bankruptcy 2: Linear types and Linear Equations; bankruptcy three: A easy version for Tomography; bankruptcy four: creation to the Fourier rework; bankruptcy five: Convolution; bankruptcy 6: The Radon rework; bankruptcy 7: advent to Fourier sequence; bankruptcy eight: Sampling; bankruptcy nine: Filters; bankruptcy 10: imposing Shift Invariant Filters; bankruptcy eleven: Reconstruction in X-Ray Tomography; bankruptcy 12: Imaging Artifacts in X-Ray Tomography; bankruptcy thirteen: Algebraic Reconstruction concepts; bankruptcy 14: Magnetic Resonance Imaging; bankruptcy 15: chance and Random Variables; bankruptcy sixteen: functions of likelihood; bankruptcy 17: Random techniques; Appendix A: historical past fabric; Appendix B: simple research; Index.