New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

3.3. PREPROCESSING 35
Figure 3.3.7: This shows the results of the TopHat Filter: the TopHat opening (see
text) is subtracted from the raw signal (shown on the left) yielding the filtered version
(on the right). Note that this method does not generate negative signals.
3.3.6 Normalization
Inter-spectrum normalization is the process of removing systematic variations
between spectra. Many different techniques exist such as “Inverse Normalization”
(Petricoin et al., 2002) or “Logarithmic Normalization” (Li et al., 2004).
Our implementation follows the idea of the most frequently used method which
is global normalization with respect to the average total ion current (TIC 2 ) 3
(Fung and Enderwick, 2002; Baggerly et al., 2003) with an important extension:
from the set of spectra to be normalized all TIC values are computed,
outliers removed and the remaining highest value (instead of the average) is
used for the actual computation.
3.3.7 Computational Complexity Analysis of Preprocessing
The complexity of the single steps of the preprocessing
Denoising: O(n log n) (Besbeas et al., 2004)
Baseline reduction: O(n) (Gao et al., 2003)
Normalization: O(n)
(n being the number of input samples) yields a total complexity of O(n log n).
2
The TIC is the sum of the area of all peaks in a spectra.
3 “TIC of spectrum”
The normalization by the ratio R =
is reported to be superior
“Average TIC of all spectra”
to other methods tested (Norris et al., 2005; Sauve and Speed, 2004).