ABSTRACT
This chapter discusses the main aspects and place of Pade approximants in a general framework of rational functions in the mathematical literature through a large branch known as theory of approximations. It focuses on the relevance of the Pade-guided magnetic resonance spectroscopy (MRS) for tumor diagnostics in clinical oncology. Pade approximants can be computed through many different numerical algorithms, including the most stable numerical computations via continued fractions. Both Magnetic Resonance Imaging and in vivo MRS are becoming the non-invasive diagnostic methods of choice for a wide range of medical applications, particularly in oncology. The fast Pade transform (FPT) provides the first exact separation of genuine from spurious information encountered either in theory or measurements involving time signals. Improved resolution and signal-to-noise ratio as provided by the FPT could be of crucial help for improving the diagnostic yield of in vivo MRS in ovarian cancer diagnostics and for malignancies of other deep-seated, moving organs.
