1. IX International Workshop ACAT
A Matched Filter System for Muon Detection with Tilecal
R. R. Ramos1, J. M. de Seixas2 and A. S. Cerqueira3
1,2 Signal Processing Laboratory
EP/COPPE – Federal University of Rio de Janeiro
3 Federal University of Juiz de Fora

2. A Matched Filter System for Muon Detection with Tilecal
Topics
The Hadronic Calorimeter (Tilecal)
The Muon Signal
The Matched Filter System
Results
Conclusions
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A Matched Filter System for Muon Detection with Tilecal

3. A Matched Filter System for Muon Detection with Tilecal
The Hadronic Calorimeter (Tilecal)
ATLAS
Tilecal is the hadronic calorimeter of ATLAS.
Tilecal comprises 192 modules.
Each module is segmented into three layers of cells.
The last layer may be used by the LVL1 trigger envisaging muon detection.
Tilecal
Barrel
Extended Barrels
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A Matched Filter System for Muon Detection with Tilecal

4. A Matched Filter System for Muon Detection with Tilecal
The Tilecal and the Muon Signal
Tilecal cells geometry:
The Level 1 trigger (LVL1) requires analogue signal summation along the three sampling layers (up to six calorimeter redout channels) of the calorimeter, forming the so called trigger tower signals.
Each adder circuit also fanouts the
information corresponding to the third layer of the calorimeter, which is used for muon detection.
As muons deposit very small energy levels in the calorimeter, muon output signal exhibits low signal-to-noise ratio.
Tilecal layers:
1st - (A# cells)
2nd - (B#, C# cells)
3rd - (D# cells)
Tilecal electronic readout:
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A Matched Filter System for Muon Detection with Tilecal

5. The Muon Signal (1) July, 2003 testbeam setup: ???
Physics events (signal)
Superposition
16 samples/event (Fast ADC – 40MHz).
Muon signal severely corrupted by background noise.
Online detection is critical.
Adding the muon outputs corresponding to a given D_cell may improve the signal-to-noise ratio.
Projective data at η = 0.45 (D2 cell) was analysed.
Mean
Pedestal events (noise)
???
Superposition
Mean
FADC problems. Only 14 samples were considered in analysis.
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A Matched Filter System for Muon Detection with Tilecal

6. The Muon Signal (2) Discriminating signal from noise:
Peak sample histograms
An usual technique consists of a simple peak detector.
An efficiency above 88.0% is obtained for a false alarm probability of 10.0%, considering the summation of the two signals of the same D_cell.
Using a single muon output results in an efficiency higher than 70.0% for the same 10.0% false alarm probability.
Adding the two signals improves the detection efficiency and is considered in the matched filter system development.
Receiver Operating Characteristic (ROC)
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A Matched Filter System for Muon Detection with Tilecal

7. A Matched Filter System for Muon Detection with Tilecal
The Matched Filter System (1)
The detection problem can be modeled as the classical decision rule between two hypothesis, where n[k] is considered a zero-mean additive white gaussian noise with variance N0/2 and s[k] is the signal to be detected.
H1: r[k] = s[k] + n[k] , k = 1,…,K
H0: r[k] = n[k]
We make use of the orthonormal expansion of s[k], the well-known Karhunen-Löeve Series. Considering Ks the auto-correlation matrix of s[k], we have
Ks.Q = Q.λ , Ks = E[s.sT]
Q – matrix of orthonormal eigenvectors qi
λ – matrix of diagonal eigenvalues λi
A = QT.s , A – 1,…,K projections
Using the new orthonormal basis spanned by Q, the signal sM[k] can be reconstructed by truncating the series in the M-ary term.
sM[k] = Q.A , A – 1,…,M projections
Q – 1,…,M eigenvectors or principal components (PCAs)
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A Matched Filter System for Muon Detection with Tilecal

8. A Matched Filter System for Muon Detection with Tilecal
The Matched Filter System (2)
Both signal s[k] and noise n[k] processes are considered multivariate Gaussians so that the classical matched filtering algorithm for random processes can be adapted to this problem.
Instead of using the signal s[k] (not available), we use r[k] under the hypothesis H1. The algorithm is derived by computing the following likelihood ratio:
The detection is made by comparing this ratio result with a threshold η (Neyman-Pearson rule).
We can take the natural logarithm of the likelihood ratio, resulting in an optimal receiver
The Øi are the eigenvectors qi. M = 14. K = 1,…,14.
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A Matched Filter System for Muon Detection with Tilecal

9. A Matched Filter System for Muon Detection with Tilecal
Results (1)
The covariance matrix Kn of the background noise n[k] shows that it´s not white.
Kn before whitening filter
The matched filter is considered optimal in the sense of the signal-to-noise ratio if the signal to be matched is corrupted by white noise.
Kn after whitening filter (training set)
At this point, a whitening filter for proper treatment of the background noise is necessary.
That is made by an orthogonal transformation equivalent to the following
Kn after whitening filter
(testing set)
(similarity transformation)
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A Matched Filter System for Muon Detection with Tilecal

10. A Matched Filter System for Muon Detection with Tilecal
Results (2)
ROCs with whitening filter
The development of the matched filter is normally performed considering the new signal r*[k] (after whitening).
The overall performance of the detector grows as we decrease the number of PCAs in both cases (with or without whitening filter).
ROCs without whitening filter
The efficiency with the whitening filter is better, reaching 93.5%, when compared to peak detector (89.0%), for a fixed 10.0% false alarm probability.
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A Matched Filter System for Muon Detection with Tilecal

11. Overall Performance Comparison
Results (3)
We considered a deterministic approach by designing a matched filter that uses the mean signal of hypothesis H1 (muon signal) as the signal to be matched.
Overall Performance Comparison
At this point, we have three approaches to be compared: the peak detector, and both stochastic and deterministic matched filters.
The stochastic matched filter has the best performance of the three approaches.
10.0% False Alarm Probability
Peak Detector
88,5%
Deterministic Matched Filter
90,5%
Stochastic Matched Filter (whitening)
93,5%
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A Matched Filter System for Muon Detection with Tilecal

12. A Matched Filter System for Muon Detection with Tilecal
Conclusions
We developed a matched filter system that reached an efficiency of 93.5% (for 10.0% false alarm probability). A whitening filter was also designed as part of the system.
The matched filter system using whitening filter outperforms a peak detector based system that is being considered by the Tilecal collaboration.
The development of an online system is being considered to be part of the ATLAS experiment.
The use of neural networks is also being considered. Preliminary results are promising.
11/28/2018
A Matched Filter System for Muon Detection with Tilecal