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.
Author(s): Carlo Ciulla
Edition: 1
Publisher: Medical Information Science Reference
Year: 2009
Language: English
Pages: 641
City: Hershey, PA
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
