By Charles L. Epstein
On the center of each scientific imaging know-how is a worldly mathematical version of the size method and an set of rules to reconstruct a picture from the measured facts. This booklet presents an organization starting place 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 procedure, it additionally covers many vital analytic options and methods utilized in Fourier research, imperative equations, sampling thought, and noise research.
this article makes use of X-ray computed tomography as a "pedagogical laptop" to demonstrate very important rules and accommodates broad discussions of historical past fabric making the extra complicated mathematical themes obtainable to readers with a much less formal mathematical schooling. The mathematical thoughts are illuminated with over 2 hundred illustrations and various workouts.
New to the second one version are a bankruptcy on magnetic resonance imaging (MRI), a revised part at the dating among the continuum and discrete Fourier transforms, a brand new part on Grangreat s formulation, a stronger description of the gridding strategy, and a brand new part on noise research in MRI.
viewers The e-book 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 knowing of calculus, linear algebra, and uncomplicated mathematical research.
Contents Preface to the second one variation; Preface; tips on how to Use This e-book; 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 strategies; bankruptcy 14: Magnetic Resonance Imaging; bankruptcy 15: chance and Random Variables; bankruptcy sixteen: purposes of likelihood; bankruptcy 17: Random procedures; Appendix A: heritage fabric; Appendix B: simple research; Index