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

3.3. PREPROCESSING 31
mix (external standard) used are important for reliable results. Not only
the zero-point of the particular machine is determined, but also machine
specific transformations (machine dependent constants, see for example
Equation 3.2.4). Once these parameters are determined correctly
the measurement errors are corrected automatically during acquisition
within the machines hardware.
Shifts in intensity direction (I) A biological sample (e.g. blood) automatically
undergoes some changes in its biochemical content, mainly
caused by proteases (see section 4.1.1). Furthermore, when mixed with
the so-called matrix, a quite inhomogeneous mixture forms, which then
becomes the final sample, put into the MS machine. Within this inhomogeneous
sample there exists so-called sweet spots where the density of
proteins is much higher than average. If now the laser beam hits these
sweet spots, the intensity of these molecules increases excessively.
3.3.3 Our Approach
In the following, we describe the algorithms we have developed (or modified
to fit our needs) to step-by-step recover the original signals available in the
sample put into the MS machine. The overall procedure is as follows:
Algorithm 1 Preprocessing
Require: Raw Spectrum as x, y value pairs
Apply wavelet-based de-noising
Apply tophat-based baseline reduction
Apply normalization
return Preprocessed spectrum
3.3.4 Denoising
Denoising the raw data X tries to remove whatever noise (ɛ) is present in X
while retaining whatever signal S is present. (Note baseline removal baseline
is handled separately - see section 3.3.5.) This is not to be confused with
smoothing which removes high frequencies present in the data and retains
low ones opposed to denoising which attempts to remove whatever noise is
present. Denoising generally yields better results in subsequent steps of the
analysis workflow, since some general assumptions about smoothness can be
taken. However, in practice most of the noise in MALDI-TOF spectra is
indeed contained in the high-frequency component of a spectrum. This is
mainly due to a number of factors, such as electrical inference, random ion
motions, statistical fluctuation in the detector gain or chemical impurities (see
e.g. (Shin et al., 2007)). There are several (heuristic) approaches for noise
reduction in the literature such as moving average filters (Liu, Krishnapuram,
Pratapa, Liao, Hartemink and Carin, 2003), Gaussian kernel filters (Wang,
Howard, Campa, Patz and Fitzgerald, 2003), or PCA (Statheropoulos et al.,
1999). However, most of these (parametric) noise reduction approaches have
been established based on empirical insights and the parameters need to be
fine-tuned to make the method work properly - this is always case sensitive
and time consuming.
Our studies have shown that the approaches mentioned above are not very
well suited for reducing noise in MALDI/SELDI-TOF spectra: for example,