High-Resolution Signal Processing in Magnetic Resonance Spectroscopy for Early Cancer Diagnostics

This paper is on the theory and practice of spectral analysis as it applies to the quantification of a wide class of biomedical time signals. The presented methodology is general and can be applied to many other interdisciplinary fields that need not necessarily overlap with biomedicine. The principal method selected for this challenging task of solving inverse synthesis-type problems in data interpretation is the fast Pade transform (FPT). This method, which can autonomously pass from the time to the frequency domain with no recourse to Fourier integrals, represents a novel unification of the customary Pade approximant and the causal Pade z-transform. The FPT automatically and simultaneously performs interpolation and extrapolation of the examined data. The idea is to synthesize time signals in a search for an adequate explanation of the observed variation in studied phenomena. This consists of composite effects with the aim of finding a subclass of simpler constituent elements related to the fundamental structure of the examined system, which produces a response to external perturbations. Such decomposition of complicated effects into simpler ones is the heart of the problem of quantifying time signals through their parametrizations. Finding a relatively small number of fundamental parameters eliciting poles and zeros, which could capture the main features of the investigated system associated with a given time signal, is of paramount theoretical and practical importance. In this way, theoretical explanations of phenomena involving time signals exhibit a great potential to simplify the initial task and coordinate its various parts by the decomposition analysis of observed composite phenomena. As such, remarkably, the theory of time signals becomes an essential complement of the corresponding measurements. This complementarity does not stop with theoretical explanations and interpretations. It also provides practical tools that enable interpolation, where measured data have not been recorded, and extrapolation to the ranges where predictions could be made about the possible behavior of the system under study. Measurements in this field yield time signals, but it is the theory that provides frequency spectra and decomposition of encoded data into their constituent fundamental elements. Such inverse problems are difficult due to mathematical ill-conditioning, and the possible solutions are further hampered by inevitable noise. This type of problem, known as quantification, spectral analysis or harmonic inversion, can be solved by the FPT for any theoretically generated/simulated time signals or experimentally measured data. The obtained solutions gain in their value by the manner in which the accompanying and unavoidable problem of noise is solved. This is done by unequivocal disentangling of the genuine from spurious information using the concept of Froissart doublets. Spurious information is precisely identified by strong coupling of unphysical poles and zeros through their strict coincidences and zero-valued amplitudes. Such pole zero confluences are totally absent for physical, genuine resonances. Hence, exact noise separation is a novel paradigm in data analysis. In the reported thorough illustrations on magnetic resonance spectroscopy for diagnostic purposes in clinical oncology, special attention is paid to current obstacles in this problem area of medicine. Our aim is to demonstrate the potential usefulness of the Pade-optimized quantification for the analysis and interpretation of encoded time signals typical of normal and malignant samples from ovarian cyst fluid, as well as from breast and prostate tissues.