Title: A Matched Filter System for Muon Detection with Tilecal
1IX 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
2Topics
- The Hadronic Calorimeter (Tilecal)
- The Muon Signal
- The Matched Filter System
- Results
- Conclusions
3The 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
4The Tilecal and the Muon Signal
- 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
5The 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.
6The 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)
7The 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)
8The 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.
9Results (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)
10Results (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.
11Results (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.
12Conclusions
- 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.