By Charles L. Epstein

On the middle of each clinical imaging know-how is a worldly mathematical version of the size method and an set of rules to reconstruct a picture from the measured information. This publication offers a company origin within the mathematical instruments used to version the measurements and derive the reconstruction algorithms utilized in such a lot imaging modalities in present use. within the procedure, it additionally covers many vital analytic strategies and strategies utilized in Fourier research, imperative equations, sampling thought, and noise research.

this article makes use of X-ray computed tomography as a "pedagogical desktop" to demonstrate vital principles and accommodates broad discussions of heritage fabric making the extra complex mathematical subject matters available to readers with a much less formal mathematical schooling. The mathematical ideas 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 better description of the gridding procedure, and a brand new part on noise research in MRI.

viewers The booklet is suitable for one- or two-semester classes on the complicated undergraduate or starting graduate point at the mathematical foundations of contemporary 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 booklet; Notational Conventions; bankruptcy 1: Measurements and Modeling; bankruptcy 2: Linear versions and Linear Equations; bankruptcy three: A easy version for Tomography; bankruptcy four: creation to the Fourier remodel; bankruptcy five: Convolution; bankruptcy 6: The Radon remodel; 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 innovations; bankruptcy 14: Magnetic Resonance Imaging; bankruptcy 15: likelihood and Random Variables; bankruptcy sixteen: functions of likelihood; bankruptcy 17: Random methods; Appendix A: history fabric; Appendix B: uncomplicated research; Index.