1 Introduction
Tunka-Rex is an antenna array, which measures the radio emission of the air showers produced by cosmic rays with energies above 100 PeV in the frequency band of 30-80 MHz Bezyazeekov:2015rpa . Tunka-Rex requires external trigger and operates jointly with the non-imaging air-Cherenkov light detector Tunka-133 Prosin:2014dxa and the scintillators of Tunka-Grande Budnev:2015cha .
The main background at the Tunka-Rex location is the Galaxy. However there are many sources of non-white and non-stationary background in the Tunka Valley. Due to this we use two different approaches: matched filter with predefined signal template and neural network with optimized convolutional filters.
2 Matched filter and autoencoder for signal reconstruction
In the present work we use 650 000 samples of measured Tunka background and 25 000 CoREAS simulations folded with Tunka-Rex hardware response. We use single polarization () and following upsampling rates: 64 for matched filter and 16 for neural network. The position of peak is defined with standard method using Hilbert envelope Bezyazeekov:2015rpa .
Matched filter (MF) convolutes template with input trace and the maximum of the convolution defines the position of the peak. Templates are obtained from averaging of many CoREASHuege:2013pro simulations. In the present work we use template with length of 60 ns (see Fig. (1
)). The threshold is defined as 5% probability of false positive. Amplitude is estimated as the function of the square root of cross-correlation. The MF is implemented in Aguer Offline
Abreu:2011pro and tested on the set of simulated events. MF is able to reconstruct pulses with lower amplitudes and features resolution of arrival direction similar to standard method. The distribution of reconstructed events and arrival directions can be seen in Fig. (2).At the next step we use neural network which called autoencoder (AE). AE based on 1D convolutional layers with rectified linear unit and max pooling after convolution layer. Binary cross-entropy is used as a loss function. For minimization of the loss, all data should be normalized in [0;1] range and baseline always should be put on 0.5 level, what helps the AE to extract features from noise.




Structure of AE is defined by the following: depth () and number of filters per layer () are free parameters. -th encoding layer () is described by the following: , , where is a size of the -th filter, is a number of filters per layer. and are free parameters; is minimal size of layer (correspoding to few ns).
To assess the quality of the networks we have introduced 2 metrics: efficiency: , namely fraction of events passed the threshold; and the purity: , namely fraction of events with reconstructed position of the peak
ns. Networks with 3-4 layers show similar result, only addition of the 5th layer increases of the purity. Networks with 5 layers have a large number of degrees of freedom which leads to overfitting with our limited size of the training dataset.
3 Summary
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We have improved Tunka-Rex signal reconstruction by implementing matched filter and autoencoder. New methods show promising results in the lowering of the threshold. We will improve current results by extending the library of templates for matched filter and optimization of autoencoder architectures.
Acknowledgements
This work is supported by the Helmholtz grant HRSF-0027, the Russian Federation Ministry of Education and Science (Tunka shared core facilities, unique identifier RFMEFI59317X0005, 3.9678.2017/8.9, 3.904.2017/4.6, 3.6787.2017/7.8, 3.6790.2017/7.8), the Russian Foundation for Basic Research (Grants No. 16-02-00738, No. 17-02-00905, No. 18-32-00460). In preparation of this work we used calculations performed on the HPC-cluster Academician V.M. Matrosov and on the computational resource ForHLR II funded by the Ministry of Science, Research and the Arts Baden-Württemberg and Deutsche Forschungsgemeinschaft. The work presented in Section 2 of this paper was funded by the Russian Science Foundation (the grant No. 18-41-06003).
References
- (1) P. A. Bezyazeekov et al., Nucl. Instrum. Meth. A 802, 89 (2015)
- (2) V. V. Prosin et al., Nucl. Instrum. Meth. A 756, 94 (2014).
- (3) N. M. Budnev et al., Bull. Russ. Acad. Sci. Phys. 79, 395 (2015) [Izv. Ross. Akad. Nauk Ser. Fiz. 79, no.3, 430 (2015)].
- (4) T. Huege et al., AIP Conf. Proc. 1535, 128 (2013), arXiv:1301.2132 [astro-ph.HE].
- (5) P. Abreu et al., Nucl. Instrum. Meth. A635, 92 (2011), arXiv:1101.4473 [astro-ph.IM].
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