Biomedical Engineering Reference
In-Depth Information
2.2. Peak Detection
Having understood the nature of a TOF-MS spectrum, we are ready to set
out to detect peaks. We will overview the logic of the peak detection here,
for more details, please refer to [20].
But, before we go further to derive formulas for peak detection, let
us rst introduce some notations that we will use throughout the paper.
We are going to use p(X) to denote the probability of some event X; use
p(XjI) to denote the conditional probability of X given relevant background
information I at hand. We will, when talking about probability, always
condition the statements on the background information, as the `absolute
probability' is not well posed. We will use p(X; YjI) to denote the joint
probability of X and Y , conditioned on relevant background information I
at hand.
Since a mass spectrum usually consists of a large number of peaks, to
identify them, the rst step is to put an observation window of carefully
chosen width N on the spectrum and thus isolate N data points in the
time series. We then compare the hypothesis H
1
that there is a peak in
the observation window versus hypothesis H
0
that there is no peak in the
window, i.e., just background noise. Once the comparison concludes that
there is a peak inside the window, we then estimate its position and intensity
via parameter tting by the maximum likelihood method.
It is possible sometimes that there could be more that one peak in an
observation window. This can be addressed in several ways. An easy x is to
choose an appropriate observation window width such that the window is
wide enough to conclude whether or not there is a peak in the window while
it is too narrow for more than one peak to be in the window. This works
ne when the instrument is of very high resolving power and peaks are not
severely overlapped. If the resolving power of the instrument is not very
high and peaks of nearby masses overlap resulting in a broader, fat peak, a
test on whether there are multiple peaks in the window will be necessary.
The logic of doing such a test would be similar to what we describe below
but more computationally involved. Interested readers may refer to [21].
For the moment, let us just consider two possibilities, i.e., there is either a
peak, or no peak.
From the previous study of a mass spectrum, it is easy to see that all
ions are subjected to the same instrumental function, peaks at dierent
m=z share the same characteristic shape, the peak lineshape at one m=z
and another m=z are similar up to a shift and rescaling. Let us assume that
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