Digital revolution opens amazing possibilities, but computers do not
think for us. To be responsible for the results, we must understand
what we are doing. In biomedical sciences, "we" cannot relate only to
mathematicians and engineers. Therefore, the first part of this book
gives a minimal necessary background in signal processing,
using only plain English and no equations. Starting from basic notions
like sampling of analog signals, inner product, orthogonality, and
uncertainty principle, through spectral and time-frequency methods of
signal analysis (spectrogram and wavelets), we arrive at the idea of
adaptive approximations and the basics of the matching
pursuit algorithm. Chapters 6 and 7 summarize major advantages and
caveats related to its
applications, with references to examples from Part II.
Each of the applications presented in Part II explores some particular
and unique feature of the matching pursuit. Starting from the explicit
parameterization of signal structures in terms of their amplitudes,
time widths and time and frequency centers, through high-resolution and
robust estimates of time-frequency energy density and their averages in
event-related paradigms, to selective estimates of the energy of
relevant structures, which improve the sensitivity of pharmaco-EEG and
stability of EEG inverse solutions. Similar to Part I, these
presentations are basically equation-free. Software used in these
studies is freely available from EEG.pl
For the mathematically oriented readers, Part III introduces formally
adaptive approximations and related technical issues, including the
mathematical tricks necessary in efficient implementations of the
matching pursuit algorithm.
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