Recapitulation of Pad´e-optimized processing of biomedical time signals - Signal Processing in MRS with Biomedical Applications - page 388

doublets) to unequivocally distinguish true from spurious resonances,
thus establishing the exact signalnoiseseparation,

•Unambiguously resolves overlapping peaks and retrieves weak resonances
with small peak areas (low concentrations in MRS),

•Obtains the amplitude d k of each resonance separately by using only one
frequency (ω k ) at a time, rather than including all the found frequencies
{ω m

}(m = 1, 2,...,k−1,k,k + 1,...) as done by the HLSVD in which
inadequate estimates for ω m (m = k) can partially or totally undermine
the accuracy of the computed d k ,

•Derives each amplitude d k from an analytical expression, in contrast to
the HLSVD where this is performed numerically by solving a system of
linear equations that invokes additional roundoff errors,

•Handles Lorentzian and nonLorentzian spectra on the same footing
by modeling the signal as a sum of K damped complex exponentials
with either stationary/constant amplitudes (distinct ω k 's only) or time
dependent polynomial amplitudes (equal and distinct ω k 's), and thereby
surpasses the HLSVD which is limited exclusively to pure Lorentzian
spectra,

•Provides strikingly robust and completely stable convergence for varying
fractions of the full signal length, yielding reasonable estimations of
the main resonances even for severely truncated signals, as opposed to
other parametric estimators that oscillate in an unwieldy manner before
eventually converging,

•Can crossvalidate all the found estimates by its two variants, FPT (+)
and FPT (−) , with the two complementary convergence regions, inside
and outside the unit circle, respectively,

•Undergoes rigorous validation and error analysis by generating the vari
ational estimates with unique upper and lower bounds for the spectral
parameters as well as the linesshape,

•Extends naturally to multidimensional signal processing since the data
are treated as a coherent whole, in contrast to the corresponding Fourier
sequential onedimensional estimations,

•Has been validated in direct applications for oncology to MRS data as
encoded in vitro from ovarian, breast and prostate cancer.

The next and urgently needed step is to more widely apply the fast Pade
transform to a variety of time signals encoded via MRS and MRSI, especially
those emanating from patients with cancers whose detection and characteri
zation remain a major clinical challenge.