Two novel spike detection algorithms have been introduced, one exploiting spike specific fre-quency patterns and the other analyzing energy of stationary wavelet coefficients. The
per-formance of both algorithms is compared to current state-of-the-art methods based on two simulated data sets. Regardless of the used data set, both proposed approaches show superior performance. This is also visualized in Fig. 5.1, where only the SWTTEO algorithms detects all spikes correctly. Furthermore, a straightforward application to real MEA recordings has been introduced, combining a well-established method for threshold selection with the sensitivity of the SWTTEO approach.
The marginal superiority of SWTTEO over TIFCO might lead to the question what the advantage of the TIFCO algorithm is. Other than the SWTTEO, the TIFCO algorithm is a basic framework with a simple moving average filter to emphasize spike features. More sophisticated algorithms originating from image processing can be considered to further accentuate spike-specific frequency patterns. Further improvement may also be drawn from evaluating the phase of complex time-frequency coefficients. So far, only the magnitude is utilized to extract spike features. More advanced algorithms from the field of audio processing like reassigning the time-frequency plane (Auger et al., 2013) are based on the phase and may improve the performance of the TIFCO algorithm. Additionally, it is noted that using a time-frequency representation based on wavelet frames as introduced in Section 3.4 does not lead to an improved performance. This is not surprising, since spike durations are usually within a certain range, which makes fixed length windows more appropriate rather than scaled ones.
Both proposed algorithms perform reasonably well in the case of overlapping spikes without any further adjustments. However, for the TIFCO approach the length of the window function directly influences the separability of overlapping spikes, leaving room for further improvement.
For instance, the DGTSF can be computed with two windows of different length. A short one to distinguish overlapping spikes and a longer one to reduce the chance of detecting the same spike twice. The SWTTEO algorithm also does not explicitly handle overlapping spikes. Here, an additional feature extraction of corresponding wavelet coefficients as proposed by Song and Li (2015) can enhance the detection of overlapping spikes even further.
In MEA recordings the absolute number of spikes present is usually unknown. This com-plicates the sole usage of one of the proposed methods, since an appropriate threshold needs to be estimated. This threshold can be based on the amount of noise present in the original signalf, but can also depend on noise present in the decision variabley. Further, approaches independent of noise levels, like evaluating the energy of spike indicators in the decision variable y might lead to better threshold estimates. Only if these threshold estimates are reliable, the spike detection algorithms TIFCO and SWTTEO can be evaluated on real data-sets.
Peak Detection for MALDI Mass
Spectrometry Using Frame Multipliers
6.1 Introduction
Matrix assisted laser desorption ionization (MALDI) is a widely used form of imaging mass spectrometry, analyzing molecular compositions of tissue sections as described in more detail in Section 1.3. Following these introductory remarks, the processing of MALDI imaging data can be structured as shown in the schematic diagram in Figure 6.1. This pipeline is proposed by Alexandrov et al. (2010) and has been modified to include all preprocessing steps.
First, initial preprocessing includes baseline removal, spectra smoothing and normalization.
Obtained spectra exhibit an intensity offset for lowerm=zvalues which originate from resulting clusters of the applied matrix during ionization (Sun and Markey, 2011). This offset is called baseline and might differ for each spectrum. Sophisticated algorithms for baseline removal are based on asymmetric least squares (de Noo et al., 2006), wavelets (Sun and Markey, 2011) or top hat filters (Sauve and Speed, 2004). After removing the baseline, Deininger et al. (2011) illustrated the advantages of normalizing MALDI imaging data spectra wise. A frequently used normalization procedure is the total ion count (TIC) normalization, which is shown to reduce artifacts resulting from matrix inhomogeneities. Spectra smoothing is also a quite commonly used preprocessing approach (Bauer et al., 2011; Du et al., 2006; Shin et al., 2010; Sun and Markey, 2011; Wijetunge et al., 2015; Yang et al., 2009). Such methods include wavelet based denoising (Coombes et al., 2005b; Kwon et al., 2008; Shin et al., 2010) and Savitzky-Golay or Gaussian filters (Yang et al., 2009).
Spectra Preprocessing
Peak Picking
Edge-Preserving Denoising
Further Analysis like Segmentation or Clustering
Baseline Removal Normalization Spectra Smoothing
Selection of Relevant Peaks
Smoothingm=zImages
Grouping Spectra
Figure 6.1:MALDI processing pipeline (adapted from Alexandrov et al., 2010, Scheme 1).
After preprocessing peak picking algorithms detect prominent peaks in mass spectra, se-parating peaks corresponding to molecules from noise. This noise might arise from varying thickness of the applied matrix, artifacts resulting from ion suppression or from electronic noise (Deininger et al., 2011). Shin et al. (2010) showed that the variance of the noise is larger in lower mass regions and decreases with increasingm=zvalues. This makes accurate peak picking quite challenging, since any further analysis like spatial segmentation or clustering groups of similar spectra are based upon the detected peaks. After selecting prominent peaks, Alexandrov et al.
(2010) demonstrated that smoothingm=z images greatly enhances segmentation results. This is also confirmed and further improved by Kobarg (2014).
The number of proposed peak picking algorithms is quite large with highly diverse approaches.
Early MALDI peak picking approaches are based on simple local maxima (Breen et al., 2000) or fitting Gaussian distributions to mass peaks (Kempka et al., 2004). More advanced algorithms make use of the continuous wavelet transform (CWT) (Antoniadis et al., 2010; Du et al., 2006;
Lange et al., 2006) or the discrete wavelet transform (Alexandrov et al., 2009; Coombes et al., 2005b; Kwon et al., 2008). Especially the CWT approach based on ridges and zero-crossings of wavelet coefficients have gained recent popularity (Antoniadis et al., 2010; Du et al., 2006;
Zhang et al., 2015). Two independent comparisons of MALDI peak picking algorithms favor wavelet approaches over other conventional methods (Bauer et al., 2011; Yang et al., 2009).
Wijetunge et al. (2015) recently introduced a new peak detection algorithm. Their approach has shown superior performance compared to the ridge line wavelet approach from Du et al.
(2006), the discrete wavelet transform based algorithm from Coombes et al. (2005b) and a Bayesian approach based on adaptive regression kernels (House et al., 2011). Simulations were performed on a publicly available data set, mimicking the features of real MALDI-TOF data. This makes the Wijetunge approach an ideal candidate to verify performance of the newly proposed peak picking algorithm.
The peak picking algorithms described above are all based on spectra wise peak picking.
Spatial information, however, might improve the peak picking process. Large peaks which are spatially surrounded by small peaks might be more likely to be ignored. In contrast, a relative small peak in a neighborhood of larger peaks might be relevant. Alexandrov and Bartels (2013) introduced an algorithm which detects peaks not spectra wise, but in correspondingm=zimages.
This is shown to evidently improve the sensitivity of peak picking algorithms compared to other classical spectra wise methods (Alexandrov and Bartels, 2013, Fig. 5).
The algorithm proposed in the following is also based on spectra wise peak detection, but can be modified to include spatial information. The combination of spectra wise peak picking and spatial awareness reduces the second and third steps in Figure 6.1 into a single step. This implies, that the proposed algorithm edge-preservingly smooths m=z images while detecting peaks.
Furthermore, the algorithm is designed such that preprocessing spectra becomes obsolete. By dividing spectra into small sections baseline effects, for example, can be sufficiently suppressed by the algorithm. Essentially, the proposed algorithm inherently combines the first three pipeline steps in Fig. 6.1 into a single step, reducing computational complexity significantly.