<title>Spectral decomposition by wavelet approximation to the Karhunen-Loeve transform</title>

Abstract

There are a wide variety of reasons to link spectroscopy with time-series analysis1 and hence with the theory of random processes. While it remains true that the dominant harmonic analysis of spectroscopy is distributional Fourier theory, there are nonetheless good rationales for exploring other decompositions such as the one explored here (the canonical decomposition). One reason which motivates us the the necessity of discriminating tissue types by color spectrum. rfo do this efficiently, one seeks to mininiize the number of characteristic discriininants which describe the spectrum. By treating the spectrum as an instance of a random process, it is well-known that the eigenvalues ) of its canonical decomposition (or Karhunen-Loeve decomposition) , when ordered in decreasing order () )'2 )3 . . .) will typically decay very rapidly, and it follows that usually only the first few (ordered) eigenvalues are needed to characterize the spectrum.