A Matched Filter System for Muon Detection with Tilecal

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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
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Topics

• The Hadronic Calorimeter (Tilecal)
• The Muon Signal
• The Matched Filter System
• Results
• Conclusions

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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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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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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 ? 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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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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The Matched Filter System (1)

• The detection problem can be modeled as the
  classical decision rule between two hypothesis,
  where nk is considered a zero-mean additive
  white gaussian noise with variance N0/2 and sk
  is the signal to be detected.

H1 rk sk nk , k 1,,K H0 rk nk

• We make use of the orthonormal expansion of
  sk, the well-known Karhunen-Löeve Series.
  Considering Ks the auto-correlation matrix of
  sk, we have

Ks.Q Q.? , Ks Es.sT
Q matrix of orthonormal eigenvectors qi ?
matrix of diagonal eigenvalues ?i
A QT.s , A 1,,K projections

• Using the new orthonormal basis spanned by Q,
  the signal sMk can be reconstructed by
  truncating the series in the M-ary term.

sMk Q.A , A 1,,M projections Q 1,,M
eigenvectors or principal components (PCAs)
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The Matched Filter System (2)

• Both signal sk and noise nk 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 sk (not
  available), we use rk 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 ? (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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Results (1)

• The covariance matrix Kn of the background noise
  nk shows that its 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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Results (2)
ROCs with whitening filter

• The development of the matched filter is
  normally performed considering the new signal
  rk (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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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.

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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.