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.

This research monograph has the following main theme. Given an interpolation function, which is supposed to determine an estimate of the unknown signal value, the reader can use the traditional approach (traditional interpolation function) to estimate the numerical value of the signal. Alternatively, the reader can follow the theoretical developments offered in the book and so design, on the basis of the unified theory described in the book, three new interpolation functions with improved approximation capabilities. That means, that under the unified theory, the book offers three new classes of interpolation functions with improved approximation capabilities of the true and unknown signal to estimate. These works were published in the year 2011 and submitted for peer review and they are now presented to the public through this new publication. There are likely to be three main types of readership of this research monograph. The primary readership is composed of users of libraries which may adopt the book as reference. The secondary readership is composed of the population of instructors/professors of a course in one of applied mathematics, signal-image interpolation, signal-image processing, biomedical imaging and/or biomedical engineering academic disciplines. In such case, the book can be used as an additional educational resource to be available both to undergraduate and graduate students, in order to assign homework and/or projects to be included in the coursework. The tertiary readership is composed of apprentices and/or passionate of math. In such case, the book would be used to employ time while following the desire of intellectual enrichment. The apprentices and/or passionate of math would study the methodology of the unified theory, would apply the unified theory such to design new interpolation functions, and should there be the desire of furthering the interest, the apprentice and/or passionate would proceed further to the analysis of the results, and possibly into the discussion and the dissemination of the knowledge made out of this book.

The approach of this book is research-like because initiates the readers process of understanding of the science problem in computing disciplines with a focused practical approach which is driven through the implementation in source code of the theoretical concepts. The combination of structured programming techniques with Graphical User Interfaces and routines employed for data visualization make also possible the discovery of new concepts, which are related to the practicality of the science problem being addressed. Such combination broadens the array of capabilities and skills acquired by the readers and it is also useful to understand the issues in the system development counterpart of the computing project. Combining computing in science settings with system development broaden the array of knowledge provided through the lecture. The treatment of the programming details is expansive and corroborated with explanations of the ANSI C/Visual C++/OpenGL coding along with pictures of the Graphical User Interfaces at work with the OpenGL windows for data visualization. Topics: 1. Whittaker-Shannon interpolation formula 2. k-Space Sampling 3. Direct and inverse Fourier Transformations 4. SRE-based interpolation functions 5. Flow charts of the Graphical User Interface 6. Booth Algorithm for binary multiplication 7. Rotation translation of 3D volumes 8. Artificial Neural Network for pattern recognition 9. Graphical User Interfaces 10. Data randomization 11. Creation of artificial data sets 12. OpenGL connection to Visual C++ to display three 2D composite views The source code which allows to build the Computer Science Applications described in the book is available for download at: http: //www.sourcecodewebsiteCarloCiulla.com

Functional Magnetic Resonance Imaging (FMRI) is currently acquired in Time Series to detect non-invasively, in-vivo functional activity of the human brain, thus determining four dimentional data sets. Although detectable, due to the short time in betweeen the acquisition of the brain volumes, head motion is usually minimal, however its correction is quite relevant to the consistency of the analysis of the FMRI data. This book presents methodology and technology for registering FMRI Time Series. Math formulations are given along with software engineering descriptions of the algorithms employed for the specific task of FMRI alignment. The book also presents the code that implements the methodology, which was written combining ANSI C, Open GL and Matlab. The intended audience of this work is composed by undergraduate and graduate students in academic disciplines within the domain of computer science applications, applied signal processing and computational engineering. Nevertheless this book is intented for anyone in the interests of how computer science, mathematics and engineering may combine together to forge the developmental effort in the quest for the solution of a technical challenge.