Quantification in Signal Processing for Magnetic Resonance Spectroscopy

ISBN-13: 9781584887744 / Angielski / Twarda / 2027 / 416 str.

Dzevad Belkic

Opis

This interdisciplinary book simultaneously deals with three selected fields. Specifically, it presents a joint framework with the unified quantum-mechanical theories of resonant scattering, spectroscopy, and signal processing. Both the standard and non-standard analyses are expounded by encompassing the key ingredient of the S- and R-matrices, variational principles, complex coordinate scaling, wave packet propagation, Fredholm determinants, finite-rank separable expansions, filter diagonalization, the Lanczos algorithm, and the Pad methodology. The highly developed mathematical theory of rational functions with the traditional Pad approximant as the leading proponent is advantageously exploited. Remarkably, this single strategy can be efficiently employed for vastly different tasks, ranging from optimal solutions of the major quantum-mechanical enquiry -- the eigenvalue problems for determining the state and structure of the investigated generic systems via acceleration of slowly converging series -- to powerful transformations of divergent into convergent perturbation expansions in a variety of applications. Moreover, accuracy, stability, and robustness put the Pad method at the forefront of the multitude of the existing solvers of the so-called inverse mathematically ill-conditioned problems. The analyzed theoretical formalism is mathematically and physically rigorous with the added value for wide, practical applications. It can be used with equal or comparable success in optimally quantifying resonances in physics, chemistry, biology, and medical diagnostics as well as in the applied area of signal processing. The overall scope and structure of this book is systematically and methodologically presented in a way to be maximally suitable for graduate students and researchers in the above-mentioned basic and applied sciences.

New quantum mechanical methods in spectral analysis offer significant advantages, including enhanced resolution and more comprehensive analysis of individual spectral peaks. This book describes the novel applications of these methods to signal processing across a wide range of interdisciplinary research fields. These methods allow researchers to evaluate data with an accuracy that is not possible with conventional methods. Focusing on applications in various areas of physics, such as accelerator physics and fusion physics radiation oncology, the text critically compares new and established methodologies based on a detailed analysis of experimental results obtained from each method.