Improved signal and image interpolation in biomedical applications: the case of magnetic resonance imaging (MRI)

Carlo Ciulla160566202X, 9781605662022, 9781605662039

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.

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Table of contents :
Foreword……Page 11
Preface……Page 13
Acknowledgement……Page 20
Preamble: On the Philosophical Basis Underlying Unifying Theory……Page 22
Magnetic Resonance Imaging and the Signal-Image Processing Techniques Developed Under the Umbrella of the Unifying Theory……Page 28
The Intuition……Page 50
The Conception of the Intensity-Curvature Functional……Page 58
Assessment of the Truth Foreseen in the Intuition……Page 75
The Notion……Page 79
The Theoretical Approach to the Improvement of the Interpolation Error: Bivariate Linear Interpolation Function……Page 85
The Results of the Sub-Pixel Efficacy Region Based Bivariate Linear Interpolation Function……Page 99
Interpolation Procedures……Page 199
The Extension of the Theory to the Trivariate Linear Interpolation Function……Page 207
The Results of the Sub-Pixel Efficacy Region Based Trivariate Linear Interpolation Function……Page 215
Equating the Two Intensity-Curvature Terms, Before and After Interpolation Attempting to Obtain Resilient Interpolation: Trivariate Linear Interpolation Function……Page 233
On the Literature of B-Spline Interpolation Functions……Page 241
The Extension of Theory and Methodology to B-Splines……Page 250
The Results of the Sub-Pixel Efficacy Region-Based B-Spline Interpolation Functions……Page 266
On the Properties of the Unifying Theory and the Derived Sub-Pixel Efficacy Region……Page 365
The Main Innovation Determined By the Sub-Pixel Efficacy Region……Page 375
The Unifying Theory Embraces Lagrange and Sinc Interpolation Functions……Page 380
The Results of the Sub-Pixel Efficacy Region-Based Lagrance and Sinc Interpolation Functions……Page 398
On the Implications of the Sub-Pixel Efficacy Region and the Bridging Concept of the Unifying Theory……Page 498
Appendix……Page 539
About the Author……Page 639
Index……Page 640