Improved Signal and Image Interpolation in Biomedical Applications: The Case of Magnetic Resonance Imaging (MRI), 1st Edition

  • Carlo Ciulla
  • Published By:
  • ISBN-10: 1605662038
  • ISBN-13: 9781605662039
  • DDC: 616.07548
  • Grade Level Range: College Freshman - College Senior
  • 614 Pages | eBook
  • Original Copyright 2009 | Published/Released March 2010
  • This publication's content originally published in print form: 2009

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About

Overview

Advances have been made in improved signal and image interpolation that derive a unified framework, thus achieving improvement of the approximation properties of the interpolation function regardless of its dimensionality or degree. Improved Signal and Image Interpolation in Biomedical Applications: The Case of Magnetic Resonance Imaging (MRI) presents a novel approach for the improvement of the approximation characteristics of interpolation functions. A unique and original resource, this book approaches both the theory and methodology absent from most publications of its kind, a valuable inclusion for those interested in exploring the innovative approach that this reference proposes.

Table of Contents

Front Cover.
Title Page.
Copyright Page.
Dedication.
Table of Contents.
Foreword.
Preface.
Acknowledgment.
Preamble: On the Philosophical Basis Underlying the Unifying Theory.
1: Magnetic Resonance Imaging and the Signal-Image Processing Techniques Developed Under the Umbrella of the Unifying Theory.
2: On the Process Driven through Deduction, Which Starts from the Intuition, Formulates a Conception, Assesses the Truth Foreseen in the Intuition, and Finally Arrives to the Derivation of the Notion.
3: The Intuition.
4: The Conception of the Intensity–Curvature Functional.
5: The Conception of the Sub–Pixel Efficacy Region.
6: Assessment of the Truth Foreseen in the Intuition.
7: The Notion.
8: Sub–Pixel Efficacy Region of the Bivariate Linear Interpolation Function.
9: The Theoretical Approach to the Improvement of the Interpolation Error: Bivariate Linear Interpolation Function.
10: The Results of the Sub–Pixel Efficacy Region Based Bivariate Linear Interpolation Function.
11: Sub–Pixel Efficacy Region of the Trivariate Linear Interpolation Function.
12: Interpolation Procedures.
13: The Extension of the Theory to the Trivariate Linear Interpolation Function.
14: The Results of the Sub–Pixel Efficacy Region Based Trivariate Linear Interpolation Function.
15: Equating the Two Intensity–Curvature Terms, Before and After Interpolation, Attempting to Obtain Resilient Interpolation: Trivariate Linear Interpolation Function.
16: Improvement of One Dimensional B–Spline Functions.
17: On the Literature of B–Spline Interpolation Functions.
18: The Extension of Theory and Methodology to B–Splines.
19: The Results of the Sub–Pixel Efficacy Region–Based B–Spline Interpolation Functions.
20: On the Properties of the Unifying Theory and the Derived Sub–Pixel Efficacy Region.
21: Extension to Lagrange and Sinc Interpolation Functions.
22: The Main Innovation Determined by the Sub–Pixel Efficacy Region.
23: The Unifying Theory Embraces Lagrange and Sinc Interpolation Functions.
24: The Results of the Sub–Pixel Efficacy Region–Based Lagrance and Sinc Interpolation Functions.
25: On the Implications of the Sub–Pixel Efficacy Region and the Bridging Concept of the Unifying Theory.
Appendix Section.
About the Author.
Index.