smoothing window of length 1.3 ms, the sym5-wavelet gives the best mDR.
Figure 5.6 illustrates the performance of the SWTTEO algorithm with respect to smoothing windows of increasing lengths. Obviously, smoothing the output of the energy operator indeed increases the accuracy of the SWTTEO algorithm (a window length of 0 ms in Fig. 5.6 indicates no smoothing). The best performance is achieved for window lengths which are close to the spike duration. Further, the results in Figure 5.6 indicate that the performance is robust even if spike durations are not known explicitly a priori, as within the range of 1 to 2 ms the performance decrease is only marginal.
Parameter Choice for Current State-of-the-Art Algorithms
The choice of parameters for the comparison algorithms described in Section 5.3.4 is crucial for a fair comparison. Therefore, recommended values according the respective literature are empirically adjusted for optimal performance based on the HAB and the UL data set. This results in the following parameters.
The WTEO algorithm is based on the sym5 wavelet and a decomposition level of 2. Originally, the db4 wavelet is suggested by Nabar and Rajgopal (2009), however, the sym5 wavelet leads to a better performance. The SWT algorithm uses a decomposition level of 5 with the same sym5 wavelet. For the HBBSD algorithm the filter length is set to 1.4 ms and the remaining parameters are chosen as proposed by Natora et al. (2010, Sec. III.C). The PTSD algorithm requires a peak lifetime period and a refractory period, which were set to 0.5 ms and 1.2 ms respectively. The MTEO as well as the ABS algorithm do not have additional parameters.
(a)Detection rate (b)Standard deviation
Figure 5.7:Detection rate and corresponding standard deviation depending on different signal-to-noise ratios for the HAB data set.
mean detection rate (mDR) for the SWTTEO and the TIFCO methods are 82.285 and 82.094 respectively, followed by the HBBSD algorithm with 80.503, the PTSD with 78.76 and the MTEO with 77.48. The poor performance of the WTEO algorithm results from not smoothing the TEO output as well as expanding decimated wavelet coefficients. Both accentuate noisy spikes.
Second, Figure 5.8 shows ROC curves for noise levels 2Œ4; 6; 8; 10. For each algorithm, the TPR is computed by thresholding the indicator signaly to yield the desired false positive rate (FPR). Apart from the WTEO, SWT and ABS algorithm, the majority of the algorithms perform quite similar for small noise levels. The performance gap between both proposed algorithms and current state-of-the-art algorithms emerges with increasing and emphasizes the superiority of the TIFCO and SWTTEO algorithm.
5.4.2 UL Data Set
The data set from the University of Leicester has been simulated at a sampling rate of 24 kHz, requiring adjustments for minimum and maximum frequency of the TIFCO algorithm. There-fore, the parameters fmin and fmax are changed to 1 kHz and 8 kHz respectively. All other parameters remain as previously described, as empirically adjusting these parameters does not lead to significant performance improvements. Further, in order to separate overlapping spikes the analyzing window function for the Gabor transform needs to be more narrow. But, this short window may cause spikes with longer durations to be detected twice: the positive and negative
(a)D4 (b)D6
(c)D8 (d)D10
Figure 5.8:ROC curves for all tested algorithms with four different noise levelsbased on the HAB data set.
part separately. Choosing a wider window in contrast reduces the chance to detect overlapping spikes. A reasonable tradeoff can be achieved by setting the window width for the DGTSF to 3000 Hz.
Figure 5.9 shows for each algorithm the percentage of correctly identified spikes depending on the eight different noise levels of the UL data set. The HBBSD algorithm is not included since reasonable spike templates could not be found. For small as well as large noise levels both proposed methods outperform all other spike detection algorithms. At the largest noise level, both proposed methods still achieve a detection rate of approximately 80% in contrast to only 44% correctly detected spikes by the ABS algorithm. The tradeoff of the window length is the main reason why the TIFCO algorithm shows a slightly inferior performance to the SWTTEO
Figure 5.9:Detection rate of spike detection algorithms in dependance on the noise level based on the UL data set.
algorithm. Here, the length of the smoothing window for the SWTTEO algorithm does not influence the detection of overlapping spikes. As mentioned before, the results in Fig. 5.9 can be directly compared with the piecewise optimal morphological filter approach by Liu et al. (2012, Table 1). Liu et al. based their evaluations on the same data set, but only up to a noise level of 0.2. Their algorithm achieved a corresponding detection rate of 95.18%, whereas the SWTTEO approach obtains 98.56% and the TIFCO 98.27% for the same noise level (0.2). Unfortunately, there are no results for larger noise levels, but based on the detection rates it can be concluded that the performance will be inferior to both proposed approaches.
5.4.3 Runtime
The future development of microelectrode arrays with higher density require fast algorithms for spike detection. Therefore, a basic run time evaluation of both proposed spike detection algorithms is visualized in Figure 5.10. The run time is compared with the ABS algorithm which has the lowest computational complexity. For each signal length, Figure 5.10 shows the mean and standard deviation of 10 independent runs. It is not surprising that the TIFCO approach performs worst, as it has the most computational expensive steps. The SWTTEO algorithm is in the best case one order of magnitude slower than the ABS algorithm. Nonetheless, it is still feasible to use the SWTTEO algorithm whenever online spike detection (during acquisition) is required (Franke et al., 2012).
Figure 5.10:Run time comparison of both proposed algorithms and the ABS algorithm.