1. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko for JINR (Dubna) – SUBATECH (Nantes) Collaboration ALICE Week 16-20 September, 2002

2. A "New" Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko for JINR (Dubna) – SUBATECH (Nantes) Collaboration ALICE Week 16-20 September, 2002

3. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Ancestors and close relatives A. Zinchenko, “A new approach to cluster finding in muon chambers” at Muon Group Meeting, Le Mont-Dore, 25-29 March, 2002 G. Chabratova, A. Zinchenko, “A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and Its Development for the Forward Muon Spectrometer of ALICE” at VIII Int. Workshop on Advanc. Comp. and Anal. Techniq. in Phys. Res. (ACAT’2002) 24-28 June, 2002, Moscow, Russia E.A. Kolganova, E.L. Kosarev, G.A. Ososkov, “Superresolution algorithms for data analysis of discrete detectors in nuclear physics”, NIM A443 (2000) 464

4. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Overview The Muon Spectrometer Basic Ideas of Bayesian Unfolding Application to Muon Cluster Finding Results Conclusions

5. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia

6. General view of the Forward Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer

7. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia  (1S)  (2S)  (3S) Mass (MeV) 9460.37±0.21 10023.3±0.31 10355.3±0.5 Difference 560 MeV 330 MeV Physical Tasks & Requirements to MUON Tracking

8. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE Physical Tasks & Requirements to MUON Tracking Requirement to the tracking and reconstruction efficiency: mass resolution has to be < 100 MeV Requirement to the detector response reconstruction: a reconstruction algorithm has to reduce the statistical noise and does not introduce excessive smothing. A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia

9. Bayes' theorem: G. D’Agostini, NIM A362 (1995) 487 If anybody observes a single event E(effect), the probability that it has been due to the ith cause of C i, i=1,2,..,n c is proportional to the probability of cause P(C i ) times the probability of the cause to produce the effect P(E|C i ). (Lucy-Richardson method: L.B. Lucy, Astronom. J. 79 (1974) 745; W.H. Richardson, J. Opt. Soc. Amer. A 62 (1972) 55 ) A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Basic Ideas of Bayesian Unfolding

10. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer Application to the positron emission tomography. Pairs of photons are registered in coincidence by pairs of detectors. The region, where the image is reconstructed, is subdivided into pixels and different pairs of detectors form tubes. Since the number of emissions inside pixels and number of of photon coincidences are described by the Poisson statistics, the likelihood function can be written Basic Ideas of Bayesian Unfolding (cont) Maximum Likelihood - Expectation Maximization (MLEM): L.A. Shepp and Y. Vardi, IEEE Trans. Med. Im., v.1 (1982) 113 A. Zinchenko ALICE Week, 16-20 September, 2002

11. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer where - vector of pixel activities, - the mean number of emissions from the pixel j contributing to the tube i, is the number of photon pairs counted in the tube i from the pixel j, is the number of detector tubes, - number of pixels. and is jth pixel visibility from the tube i. The Expectation step of the EM algorithm is done by taking a conditional expectation of log-likelihood with respect to parameter estimates at the nth iteration and measured detector counts. The Maximization step is to take partial derivatives of the expectation, set them to 0 and solve. The new value for the jth component of the vector A. Zinchenko ALICE Week, 16-20 September, 2002 Basic Ideas of Bayesian Unfolding (cont)

12. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer “Journey to the Center of a Rat’s Heart’’ (Sci. Fi., PG-13) “Halloween-12’’ (Horror, R) A. Zinchenko ALICE Week, 16-20 September, 2002 Some Examples From Medical Imaging

13. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer Detector: Cathode Pad Chamber (CPC). Two cathodes with pad sizes varying from (0.4x0.6) cm 2 to (10.x0.7143) cm 2. Old method: The pad charge distribution is described by two- dimensional integral of the Mathieson function and coordinates of a single track are extracted from a fit of the pad charge distribution by this function. The number of track candidates is estimated from the number of local maxima in the pad charge distribution. Amount of events with significant overlapping of signal and background induced pad charges is not negligible. Estimation of the number of track candidates from the local maxima is not sufficiently accurate and results in deterioration of coordinate resolution. A. Zinchenko ALICE Week, 16-20 September, 2002 Application to Muon Cluster Finding

14. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer ¥ New method: transform the "two- cathode fixed pad size" problem into the "one-anode plane variable pixel size" one. ¥ Find groups of adjacent pads on one cathode and overlapping with them pads on the other cathode precluster ¥ Precluster array of pixels in the anode plane with size defined by the overlap of pads on both cathodes. ¥ It is assumed that each pixel contains a track A. Zinchenko ALICE Week, 16-20 September, 2002 Application to Muon Cluster Finding

15. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer New method (cont): Iterative procedure: Track j has an initial value of energy release. Usually all 's are set to 1. with where - the expected signal on pad i for track energy releases at the k th iteration, - the track-to-pad coupling(signal on pad i from track j given by Mathieson) and - the number of tracks in the array. Application to Muon Cluster Finding(cont) A. Zinchenko ALICE Week, 16-20 September, 2002

16. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer New method (cont): after several iterations (10-15) the pixel size is decreased by two; track candidates with the lowest energy releases are removed if the total number of candidates exceeds the number of pads; interactive procedure is repeated; Algorithm stops when the pixel size becomes sufficiently small (1mm) Application to Muon Cluster Finding(cont) A. Zinchenko ALICE Week, 16-20 September, 2002

18. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer ¥ Coupling definitions: ¥ cluster_i-to-pad_j coupling: ¥ cluster_i-to-cluster_j coupling: Fitting procedure (what and how to fit) A. Zinchenko ALICE Week, 16-20 September, 2002

19. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer ¥ Minimized function: ¥ old: ¥ new: ¥ with - pad charge, f - function (integral of Mathieson function), Fitting procedure (cont) A. Zinchenko ALICE Week, 16-20 September, 2002

20. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer ¥ Cluster and hit finding - non-parametric approach; ¥ Coordinate reconstruction - parametric approach The same problem from another angle of view A. Zinchenko ALICE Week, 16-20 September, 2002

21. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Results: residuals in the non-bending plane

22. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Results(cont): residuals in the bending plane

23. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Results(cont): residuals in the bending plane

24. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Results(cont): residuals in the bending plane

25. A New Approach to Cluster Finding in Cathode Pad Chambers of the Muon Spectrometer A. Zinchenko ALICE Week, 16-20 September, 2002 Conclusions: There is a nice method of cluster finding and hit reconstruction It gives quite promising results for cathode pad chambers of the Forward Muon Spectrometer Acknowledgements: The work has been partly supported under the Protocol of International Cooperation SUBATECH-JINR 97-31 and INTAS grant 00-00538.