Introduction to the Mathematics of Medical Imaging

Häftad, Engelska, 2007

1 525 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts, and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis.This text uses X-ray computed tomography as a ""pedagogical machine"" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises.New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat’s formula, an improved description of the gridding method, and a new section on noise analysis in MRI.

Produktinformation

Utgivningsdatum:2007-10-30
Mått:152 x 229 x undefined mm
Vikt:1 365 g
Format:Häftad
Språk:Engelska
Antal sidor:794
Upplaga:2
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898716429

Utforska kategorier

Mer om författaren

Charles L. Epstein is a Professor at the University of Pennsylvania with appointments in Mathematics and Radiology.

Innehållsförteckning

Preface to the Second EditionPrefaceHow to Use This BookNotational ConventionsChapter 1: Measurements and ModelingChapter 2: Linear Models and Linear EquationsChapter 3: A Basic Model for TomographyChapter 4: Introduction to the Fourier TransformChapter 5: ConvolutionChapter 6: The Radon TransformChapter 7: Introduction to Fourier SeriesChapter 8: SamplingChapter 9: FiltersChapter 10: Implementing Shift Invariant FiltersChapter 11: Reconstruction in X-Ray TomographyChapter 12: Imaging Artifacts in X-Ray TomographyChapter 13: Algebraic Reconstruction TechniquesChapter 14: Magnetic Resonance ImagingChapter 15: Probability and Random VariablesChapter 16: Applications of ProbabilityChapter 17: Random ProcessesAppendix A: Background MaterialAppendix B: Basic AnalysisIndex.

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Introduction to the Mathematics of Medical Imaging

AvCharles L. Epstein

Häftad, Engelska, 2007

1 525 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

Produktinformation

Utgivningsdatum:2007-10-30
Mått:152 x 229 x undefined mm
Vikt:1 365 g
Format:Häftad
Språk:Engelska
Antal sidor:794
Upplaga:2
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898716429

Utforska kategorier

Mer om författaren

Charles L. Epstein is a Professor at the University of Pennsylvania with appointments in Mathematics and Radiology.

Innehållsförteckning

Preface to the Second EditionPrefaceHow to Use This BookNotational ConventionsChapter 1: Measurements and ModelingChapter 2: Linear Models and Linear EquationsChapter 3: A Basic Model for TomographyChapter 4: Introduction to the Fourier TransformChapter 5: ConvolutionChapter 6: The Radon TransformChapter 7: Introduction to Fourier SeriesChapter 8: SamplingChapter 9: FiltersChapter 10: Implementing Shift Invariant FiltersChapter 11: Reconstruction in X-Ray TomographyChapter 12: Imaging Artifacts in X-Ray TomographyChapter 13: Algebraic Reconstruction TechniquesChapter 14: Magnetic Resonance ImagingChapter 15: Probability and Random VariablesChapter 16: Applications of ProbabilityChapter 17: Random ProcessesAppendix A: Background MaterialAppendix B: Basic AnalysisIndex.