Filtering tracks in discrete detectors using a cellular automaton

Nuclear Instruments and Methods in Physics Research A329 (1993) 262-268 North-Holland NUCEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A Filtering tracks in discrete detectors using a cellular automaton A. Glaov, I. Kisel, E. Konotopskaya and G. Ososkov Joint Institute for Nuclear Research, Head Post Office, P.O Box 79, 101000 Moscow, Russian Federation Received 3 February 1992 and in revised form 1 October 1992 The study of the functioning of detectors like a multiwire proportional chamber has led to the necessity of taking into account its discrete structure and of prefiltering data before processing. The filtering method for tracks in this discrete detector based on the cellular automaton is described. Results of the application of this method to experimental data (the spectrometer ARES) are quite successful : a high degree of cleaning from noise and the restoring of missing clusters give three-fold reduction of raw data with the partial track recognition. The percentage of good events is increased and their further processing is considerably simplified and accelerated. The described cellular automaton for track filtering is suitable for parallel computing and could be also used in the on-line mode. 1. Introduction The transition from film methods in the data acquisition in bubble and streamer chambers to filmless electronic experiments required adequate changes of data handling methods. As was mentioned in Charpak's pioneering works [1], the discrete structure of such a detector as a multiwire proportional chamber (MWPC) bears sufficiently rich information about track points and its slope at each of them. Much later it was shown [2,3] that the probabilistic model of measurements also had to be changed. The reason is that the errors of measurements are in fact correlated and their distribution is not normal but box-shaped with a width specified by wire spacing. In ref. [3] the inference was made that the transition to Chebyshev metrics instead of conventional 1-2-metrics, used in least square methods, improves accuracy of track parameter reconstruction by a factor of vn, where N is the number of measurements. This result was confirmed in our previous work [4] where the detailed probabilistic and geometric analysis was fulfilled for MWPC functioning. On the basis of this analysis we suggested algorithms for the search for straight and circular tracks. The Chebyshev metrics was also applied in our work to the fast vertex search. The suggested algorithms were tested by track and vertex searching with simulated and real data from the ARES setup [7] and showed their satisfactory efficiency. All these works confirmed the fruitfulness of this approach oriented to discreteness of the detector structure and stimulated our further research. At the same time the analysis of the real experimental data obtained with the spectrometer ARES re- quired the necessity of prefiltering these data from noise hits and restoring the missing hits. In the analyed experiments the ARES spectrometer was used as a system of ten coaxial cylindrical multiwire proportional chambers (about 5000 wires) and of three cylindrical scintillator hodoscopes in a magnetic field. Due to the experimental conditions the average track radius was = 20 cm, the width of ioniation clusters ranged from one to three wires. The trigger conditions required the track passing through the target and the last chamber. The rate was about 15-30 events per second. The problem of prefiltering arose because of the high rate, the specific features of the beam duty cycle, chamber and electronics malfunctions, the presence of 5-electrons, returned tracks and other difficult-to-check reasons. As a result, we came to the well-known concept of two-stage processing : prefiltering at the first stage, which decreases significantly the redundant information, and the event recognition at the second stage. Here we consider only problems of the first stage. et us formulate the common requirements of the prefiltering procedure : - high degree of event cleaning from noise hits ; - restoring of hits missing because of chamber malfunctions ; - grouping of filtered hits according to their possible belonging to different tracks ; - simplicity and high speed of the filtering algorithm needed for their on-line implementation ; - suitability for parallel processing. The accurate consideration of the detector discrete structure and necessity to hold these requirements 0168-9002/93/$06.00 1993 - Elsevier Science Publishers B.V. All rights reserved

brought us to the idea of using the well developed methods of cellular automata. The logical rules of cellular automaton evolution are proposed on the basis of specific features of the MWPC #'. The results of successful testing of this automaton by prefiltering the data obtained with the spectrometer ARES during the search for the forbidden decay l. +- e+ e+ e - [81 and the study of the rare [91 decay Tr+-> e+v,e+e - are given. A. Glaoc et al. / Filtering tracks in discrete detectors cathode planes plane of anode wires 263 2. Specific features of MWPC Using the ARES spectrometer as an example, let us consider in the XY projection (fig. 1) two specific features of a discrete detector like a multiwire proportional chamber. First, the shape of external equipotential lines in a proportional chamber allows us to draw imaginary equidistant planes between wires perpendicular to a plane of wires. Second, due to electro-negative additives in the chamber gas the distribution function of the electron collection is box-shaped, i.e. on both sides of the wire plane there exist two planes, so that all electrons that appeare inside them are collected by a wire. But any of electrons outside them are absorbed by the gas. Both these features allow us to consider the chamber to be a chain of imaginary rectangles, each of them surrounding a signal wire. Two parallel sides of each rectangle are determined by the "equipotential" planes, two other sides are formed by the planes of maximal electron collection. Whenever a charged particle track hits a rectangle, a wire inside it produces a signal. If a track crosses a few adjacent rectangles in the chamber, they all work, forming a cluster. In the latter case the track crosses the left side of the lower rectangle and the right side of the upper one or vice versa. Otherwise it would either not have crossed all the hit rectangles or have touched one of missing ones. The most important feature of our model of the discrete detector is the possibility of solving approximately the inverse problem of the track reconstruction (fig. 1). Knowing a cluster structure, one can make conclusion about a range of possible slopes of track passing through the cluster. Besides, when the slope is fixed, the cluster structure determines a possible range of points, where the track crosses the plane of signal wires. This model is confirmed by the results presented in figs. 2-4. In these figures the dependence of the cluster width on the angle of the track passage through the wire chamber for single, double and triple clusters is #' Certainly, taking into account discrete features of another type of electronic detectors would bring us to another cellular automaton. Here we consider only the MWPC. Fig. 1. The model of cluster formation (wires are shown by bold dots). shown #. Here the angle is counted from the normal to the chamber. In the same figures the thin line is the cluster distribution for the model case, when the chamber is presented as a chain of rectangles with the maximal distance h = 1.5 mm of electron collection. As it follows from these figures, this simple model is a satisfactory good approximation for the description of cluster forming effects in the proportional chamber. The difference between the real physical processes and our simplified model is easily taken into account in the implementation of the software. 3. Construction of a cellular automaton Cellular automata [51 are discrete dynamic systems whose behavior is completely determined by local mutual relations of states of these systems. The space is a uniform grid, every cell of which contains a few bits of information. Time is increases by discrete steps. The evolution law is described by a set of rules, let us say, by a table. By means of this table every cell at each step can evaluate its new state according to the states #2 Results were obtained on the ARES setup.

264 A. Glaou et al. / Filtering tracks in discrete detectors m 150 125 U O N A C Û O U A Fig. 2. The distribution of single clusters as a function of track slope. Fig. 4. The distribution of triple clusters as a function of track slope. of its neighbors. If the appropriate set of rules is given then this easy operational mechanism is sufficient for supporting the whole hierarchy of structures and events. Cellular automata give us useful models for many fields in natural science. They created the general paradigm of parallel computations similar to Turing machines for sequential computations. One can formulate the general rules for cellular automata as follows : 1) The cell state is discrete (usually 0 and 1 although there can be automata with a larger number of states). 2) The number of neighboring cells is restricted, often they are the nearest cells. 3) The rules describing the dynamics of the evolution of the cellular automaton have usually a simple ô ô A Fig. 3. The distribution of double clusters as a function of track slope. functional form and depend on the problem to be solved. 4) The cellular automaton system is clocked, i.e. the cell states change simultaneously. et us try to create such a cellular automaton for event filtering. It has to sort out noise hits leaving only experimental points which belong to tracks. Using the well-known game "ife" terminology [6] we can formulate the task of an automaton as : - leave cells belonging to the track as living ones ; - restore as newborns the gaps on the track caused by chamber inefficiency; - eliminate (define dead) all cells which correspond to noise hits ; - divide the rest of living cells into groups, corresponding to different track candidates, on the basis of mutual neighborhood. From there, we can formulate the specific rules of the constructed automaton. First, we define the huing cell as a cluster, i.e. a continuous group of hit wires (see fig. 1). The dead cell is an empty one which does not contain any hits (remember, noise clusters should die in process of the automaton evolution). To support the vital capacity of interrupted tracks (because of chamber malfunction) it is necessary to produce new cells-"phantoms" which would correspond to real clusters if the chamber works correctly. The phantom cells can also die and be reproduced again later but we have to keep them in mind since only real clusters can appear in the final pattern. Thus in our case the cell has four states : real cluster or phantom and living or dead one. Second, we suggest the rule for determination of neighbors based on the discrete nature of our track detector. As shown above, the cluster structure defines the admissible angles of track passing. The method of

A. Glaou et al. / Filtering tracks in discrete detectors 265 neighbor determination is built on this feature. Only those clusters can be treated as neighbors in adjacent chambers, through which one can draw a track according to the admissible angles. However, there is an essential physics constraint : any track must leave the target and reach the last chamber. Therefore, we can regard as neighbors only those cells lying in adjacent chambers through which one can draw such an admissible track. From there we can also define a region of potential neighbors of the cluster as a region in the adjacent chambers that is swept up by all admissible tracks passing through the given cluster. This definition is necessary to restore clusters missed due to chamber malfunctions. Third, let us consider the rules of automaton evolution in order to reject noise leaving only true tracks. To begin with, we have to restore clusters missing because of chamber malfunction. Due to the high efficiency of chambers (98-99%) double malfunction of adjacent chambers is in fact impossible (the probability of this case is of the order of 10-4) and we can neglect such cases. In the usual case of the non-interrupted track, every cell has two neighboring cells in the adjacent chambers and lies in their overlapping regions of potential neighbors. If there is no cell in this overlapping (due to malfunction of the given chamber or electronics) it is necessary to produce a phantom cell that is a neighbor of both cells pointing to it (see fig. 5). Then we have to destroy noise clusters, i.e. cells having too few neighbors or too many of them. It is obvious that the cell lying on a single track has exactly two neigh- Fig. 5. The birth condition of cell-phantom. hors. In the case of three-track events it is quite probable that two tracks intersect. This means that the cell on the track intersecting has four neighbors (two from both sides). The probability of three tracks intersecting at one point is negligible. Thus, we have to destroy cells having less than two or more than four neighbors. The problem of the first and last chambers is a separate one. To prevent suppressing tracks from both ends, it is necessary to create imaginary chambers with numbers 0 and (N + 1). They contain neighbors supporting all cells in the real out chambers. Fourth, it is useful to treat birth and death of cells at different stages. The order of these stages is essential. If we would eliminate noise clusters at the first stage, then it could destroy the admissible interrupted tracks. Therefore it is reasonable to handle the birth at the first stage and the death at the second. This order is repeated at every step of the automaton evolution to help the interrupted tracks to survive. We can now briefly formulate the specific features of our filtering automaton (compare with the beginning of section 3): 1) Every cell is either a cluster or a phantom and therefore has four states : a real cluster or a phantom and a living cell or a dead one. 2) The cells in adjacent chambers are neighbors only if an admissible track could pass through them. 3) The cell birth occurs if this cell has at least two neighbors in different chambers. The cell death occurs in two cases : if this cell has less than two neighbors ("loneliness") or if it has more than four neighbors ("overpopulation"). 4) The evolution is clocked, i.e. all cells change their states simultaneously. Each step of the automaton evolution consists of two distinctive stages : the birth at the first stage and the death at the second one. The final stage of the automaton evolution is attainment of a stable or cyclic state. The special processing of the cyclic state is not necessary since in our case the difference between internal configurations of cyclic states consists of various numbers of phantom cells which is negligible. Therefore the attainment of the cyclic state means in practice elimination of all possible noise hits. In order to sense the automaton arrival in the stable or cyclic state we suggest calculation of the checksum CRC (cyclic redundancy check) for every generation and stop iteration in the case of the coincidence of checksums related to different generations. Remember that in the CRC method all bits of an array are considered as coefficients of a binary polynomial and bytes of the checksum are the remainder from division of this polynomial by the known polynomial of degree 16. The other features or functioning details of our automaton are just the same as for conventional cellular automaton [5].

26 6 A. Glaov et al. / Filtering tracks in discrete detectors 4. Track filtering and results of applications The cellular automaton was realied on an IBM PC/AT-386 and has been tested with real three-track events obtained during the experiment aimed at searching for the forbidden decay lt --> e+e+e - [8] and the study of the rare decay ar + -~ e +vee + e- [9]. Only ten chambers were used in this experiment. It means that every track contains on the average ten clusters. An example of application of the cellular automaton which was constructed according to the above requirements, is shown in fig. 6. Stars denote clusters eliminated as noise by the automaton. One can see in the upper part of chambers 2 and 3 (starting from center) two eliminated noise hits. The track in the lower part of the figure returned back to the detector after collision with the outer wall and this part was also rejected by the automaton. Close to this track there are 6-electron clusters in chambers 9, 11 and 12. Two of them were rejected on the basis of the information about cluster lengths #3. However, the 8-electron cluster in chamber 11 had the same length as the track cluster in this chamber. So the automaton kept both these clusters as valid. Note the missing hit from this track in chamber 10. In this chamber the cellular automaton substituted the cell-phantom. That rescued this interrupted track from demolishing. Cell-phantoms are not shown in fig. 6 since they are used temporarily only in the automaton evolution process. Chambers 7 and 8 were not used during these experiments. The advantages of the automaton are its simplicity and high speed of work. Namely, the ARES parameters and experiment conditions allow us to construct a cellular automaton with the total number of cells 1000. The number of neighbors for each cell varies from six to ten, depending on the cluster length. For every cell the procedure of looking for neighbors and determination of the cell state at the next step requires = 40 assembler instructions (basically on registers). Supposing five steps per event at the average (see fig. 7), the total number of instructions for converging to the final state is = 5 x 40 x 1000 = 2 x 10 5. Thus, for an IBM PC/AT with the speed 5 X 10 6 instructions per second the processing of one event by our automaton takes about 1/25 s #4. In fig. 7 the distribution of the number of filtering steps is shown. et us point out that the automaton needs at least two steps to make sure that its work is #3 Cluster lengths are not shown in this figure. #a We can neglect the time required to load the data, i.e. to construct the initial configuration of the cellular automaton, since it takes on the average 50 references to memory only. Fig. 6. An example of the cellular automaton application. finished (checksums coincide). About five steps are needed on the average to finish the automaton work. The curve is decreasing slowly with the number of steps because of spiral tracks and random distribution of noise hits in real events (see the long "tail" in fig. 8). In fig. 8 the distribution of the number of events according to the number of clusters in an event is shown (the thin line shows distribution after the automaton work). In the original distribution one can see that due to the preselection there are no events with the number of clusters less than 30. The long tail, caused by noise, can also be seen ranging up to 100 clusters per event. In the distribution obtained as a result of automaton working the peaks are clearly seen in the region of one- and two-track events (which, were ô E~ 3000 2500 2000 1500 1000 500 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Number of Fig. 7. The number of filtering steps. steps

A. Glaou et al. / Filtering tracks in discrete detectors 267 7000 6000 5000 0 P 4000 3000 2000 1000 Number of clusters Fig. 8. Distribution of the number of events according to the number of clusters in an event before the cellular automaton and after (thin line). left in the previous stage of processing) as well as three-track events (10, 20 and 30 clusters respectively). One can see that the cellular automaton can reject the noise quite well. Now we can naturally determine the number of tracks according to the number of clusters. Besides, the automaton can decrease the volume of data needed for further processing almost by a factor of 3 : it rejects about 20% of events being non-threetracks and decreases almost 50% of the number of experimental points from proportional chambers due to noise rejection. More explicitly the degree of cleaning from noise is shown in fig. 9. It presents the distribution of the percentage of the noise elimination by our automaton as a function of total number of noise hits in each event. As one can see, the prefiltering by the cellular automaton eliminates on the average 65-70% of the 1000 > 750 m 4 N É 500 250 0 10 20 30 40 50 60 70 BO 90 100 Rejected noise (per cent) Fig. 9. Distribution of the percentage of the final elimination. 5. Conclusion 0 0 10 20 30 40 50 Number of clusters Fig. 10. Distribution of the number of clusters in a group. total noise. The analysis of the rest of noise hits shows that they are mainly clusters from 6-electrons lying too close to tracks and having the cluster structure similar to the track clusters (see also our explanation to fig. 6). The result, which is a by-product but is very important for further processing, consists in grouping experimental points according to their possible belonging to a track. In fig. 10 there is the distribution of the number of clusters in a group marked by the automaton. One can see peaks in the region of 10 clusters (one-track group) and 20 clusters (two-track group). In some cases the automaton could not separate close or intersecting tracks. The reasons for that were : local character of the automaton, the big target sie and the relatively long distance between chambers. The method of track filtering described above is the first application of cellular automata to handling of data from multiwire proportional chambers. The results obtained with the real data are quite successful : the high degree of cleaning from noise and restoring of missing clusters lead to a threefold reduction of input information with data grouping according to their belonging to different tracks. The percentage of useful events is increased and their further processing is considerably simplified and accelerated. According to their nature the cellular automata are ideal objects for making evolution algorithms parallel. Even the minimal parallelism in our case (at least one processor per chamber) increases the speed of calculation by an order of magnitude. So the described cellular automaton for track filtering can be successfully used in parallel computers and also in the on-line mode. The special hardware implementation of the

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