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

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. 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 The intuition The conception of the intensity-curvature functional The conception of the sub-pixel efficacy region Assessment of the truth foreseen in the intuition The notion On the estimate of the interpolation function of the true pixel value : local concavity or convexity The theoretical approach to the improvement of the interpolation error The results of the sub-pixel efficacy region based bivariate linear interpolation function On the significance of the novel theory A review on interpolation procedures The extension of the theory to the trivariate linear interpolation function On the significance of the sub-pixel efficacy region On the literature of B-spline interpolation functions The extension of theory and methodology to B-splines The results of the sub-pixel efficacy region based B-spline interpolation functions On the significance of the unifying theory and the derived sub-pixel efficacy region On the literature of lagrange and sinc interpolation functions and the main innovation determined by the sub-pixel efficacy region The unifying theory embraces lagrange and sinc interpolation functions The results of the sub-pixel efficacy region based lagrange and sinc interpolation functions On the implications of the sub-pixel efficacy region and the bridging concept of the unifying theory. 'This book presents novel concepts supported through mathematics to create unique theories related to interpolation'--Provided by publisher.