Improved Signal and Image Interpolation in Biomedical Applications: The Case of Magnetic Resonance Imaging (MRI)
Date: 30 April 2011, 08:48
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Improved Signal and Image Interpolation in Biomedical Applications: The Case of Magnetic Resonance Imaging (MRI) By Carlo Ciulla * Publisher: Medical Information Science Reference * Number Of Pages: 640 * Publication Date: 2009-02-25 * ISBN-10 / ASIN: 160566202X * ISBN-13 / EAN: 9781605662022 Product Description: 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 Preamble On the Philisophical Basis Underlying the Unifying Theory Ch. I Magnetic Resonance Imaging and the Signal-Image Processing Techniques Developed Under the Umbrella of the Unifying Theory 1 Sect. I 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 Ch. II The Intuition 23 Ch. III The Conception of the Intensity-Curvature Functional 31 Ch. IV The Conception of the Sub-Pixel Efficacy Region 40 Ch. V Assessment of the Truth Foreseen in the Intuition 48 Ch. VI The Notion 52 Sect. II Sub-Pixel Efficacy Region of the Bivariate Linear Interpolation Function Ch. VII The Theoretical Approach to the Improvement of the Interpolation Error: Bivariate Linear Interpolation Function 58 Ch. VIII The Results of the Sub-Pixel Efficacy Region Based Bivariate Linear Interpolation Function 72 Sect. III Sub-Pixel Efficacy Region of the Trivariate Linear Interpolation Function Ch. IX Interpolation Procedures 172 Ch. X The Extension of the Theory to the Trivariate Linear Interpolation Function 180 Ch. XI The Results of the Sub-Pixel Efficacy Region Based Trivariate Linear Interpolation Function 188 Ch. XII Equating the Two Intensity-Curvature Terms, Before and After Interpolation, Attempting to Obtain Resilient Interpolation: Trivariate Linear Interpolation Function 206 Sect. IV Improvement of One Dimensional B-Spline Functions Ch. XIII On the Literature of B-Spline Interpolation Functions 214 Ch. XIV The Extension of Theory and Methodology to B-Splines 223 Ch. XV The Results of the Sub-Pixel Efficacy Region BasedB-Spline Interpolation Functions 239 Ch. XVI On the Properties of the Unifying Theory and the Derived Sub-Pixel Efficacy Region 338 Sect. V Extension to Lagrange and Sinc Interpolation Functions Ch. XVII The Main Innovation Determined By the Sub-Pixel Efficacy Region 348 Ch. XVIII The Unifying Theory Embraces Lagrange and Sinc Interpolation Functions 353 Ch. XIX The Results of the Sub-Pixel Efficacy Region Based Lagrange and Sinc Interpolation Functions 371 Ch. XX On the Implications of the Sub-Pixel Efficacy Region and the Bridging Concept of the Unifying Theory 471 Appendix 512 Index 613
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