Fast Hough Transform Tracking for the ALICE TPC

1. Fast Hough Transform Trackingfor the ALICE TPC C. Cheshkov 3-7 Oct 2005 TIME’05

2. Joint venture between ALICE HLT team: T. Alt, C. Loizides, G. Overbekk, D. Rohrich, T. Vik, A. Vestbo et al. and ALICE Core Offline group: J. Belikov, P. Hristov & C. Cheshkov C. Cheshkov

3. Outline • Introduction • ALICE High Level Trigger (HLT) • ALICE TPC functionality and layout • HLT tracking algorithms for TPC • Fast ‘counting’ Hough Transform (HT) tracking for TPC • Parameter space filling procedure • Parameter space variables definition • Tracking performance results • Benchmarking results • Conclusions C. Cheshkov

4. ALICE Detector Layout C. Cheshkov

5. ALICE High Level Trigger Detectors Detectors Detectors Detectors 12GB/s 12GB/s 12GB/s 12GB/s DAQ DAQ DAQ DAQ HLT HLT HLT HLT 1.2GB/s 1.2GB/s 1.2GB/s 1.2GB/s Mass Storage Mass Storage • Data rate from central PbPb collisions (dN/dy~2000-4000): 200Hz*(30Mb-60Mb)=6-12Gb/s • Max mass storage bandwidth ~1.2Gb/s • The goal of HLT is to reduce the data rate without biasing important physics information: • Event triggering • “Regions of Interest” • Advanced data compression • Requirements: • Fast and robust online reconstruction • Sufficient tracking efficiency and resolution • Fast analysis of important physics observables C. Cheshkov

6. ALICE High Level Trigger • Large computer cluster (about 400 nodes) • Off-the-shell PCs connected with high-bandwidth network • Fault-tolerant publisher/subscriber principle • FPGA co-processors for local pattern recognition • “Barrel” HLT Physics triggers: • Jets • Aim: trigger for high-Et jets • Requires: TPC tracking (+Inner Tracking System) • Charmonium spectroscopy • Aim: trigger for dielectrons • Requires: TPC and TRD tracking, TRD electron PID • Open charm • Aim: trigger for D0K • Requires: TPC and ITS tracking • Pile-up removal in p-p • Aim: reduce the size of TPC raw data by filtering out background events • Requires: TPC tracking C. Cheshkov

7. ALICE TPC E E B=0.5T • Outer and inner radii – 84 cm and 250 cm • Long. Size ~5 m • Acceptance ||<0.9 • 18 trapezoidal sectors • 72 Cathode pad readout chambers • 159 pad row ~560 000 pads • 10-bit ADC at 6MHz sampling rate • Max drift ~90 s Readout chambers C. Cheshkov

8. Central PbPb event (dN/dy~6000) Only primary tracks with Pt>1GeV/c are shown ~15-30% occupancy ~50 million ADC amplitudes ~3 million clusters ~10000 tracks in the acceptance ~50 Mbytes compressed data C. Cheshkov

9. ALICE HLT algorithms for TPC tracking • Low multiplicity (up to dN/dy~2000-3000): • Cluster finder + track follower (in Conformal Mapper space) • ~13s for dN/dy=4000 (including 4s for cluster finder) • Cluster finder implemented on FPGA • High multiplicity (up to dN/dy~8000): • Standard ‘grayscale’ Hough Transform • Satisfactory tracking efficiency • But… • High fake track rate • Resolution affected by the high multiplicity environment • Poor time performance: 1000s-2000s for central PbPb event • Fast ‘counting’ Hough Transform approach C. Cheshkov

10. Hough Transform: Highly parallelizable – FPGA implementation Computing time - massive random memory access Efficiency and resolution limitations – parameter space binning Tracking algorithm: Consider only primary tracks Neglect energy losses and multiple scattering  track model: helix crossing the origin Split TPC data in bins of pseudo-rapidity  3D2D Hough Transform Parameter space – histogram with tracks helix parameters Space-points transformed into curves corresponding to all possible track helices they can belong to Parameter space peaks are found and tracks are reconstructed Hough Transform TPC tracking Image space – TPC sector Parameter space Track curvature Emission angle C. Cheshkov

11. ‘Grayscale’ HT: Parameter space histogram incremented by raw ADC counts Parameter space bins accumulate the charge along the track trajectory Peaks: charge>threshold ‘Counting’ HT: Parameter space histogram incremented by the distance to last filled pad row Parameter space bins count the # of ‘gaps’ along the track trajectory Peaks: #gaps<threshold Hough Transform TPC tracking Pad rows Pads C. Cheshkov

12. ‘Counting’ Hough Transform • Powerful identification of good track candidates • Intrinsic TPC detector efficiency  100% • Good track candidates have ‘almost’ no gaps • Unbiased extraction of track parameters • Background does not affect the parameter space peaks • Large room for speeding up • Perform Hough Transform only for “cluster” edges and fill the entire “cluster” at once • Early fake tracks removal by accumulated # of gaps C. Cheshkov

13. Parameter Space Definition TPC sector layout • Conformal Mapping space (x,y)  =x/(x2+y2) , =y/(x2+y2) • Define two curves =const. (circles) • Tracks are represented by two points on these curves 1 and 2 • Space-points are transformed into straight lines in parameter space  Linear Hough transform •  curves chosen at middle and outer sector edge  Min correlation between variables  At first processing of TPC pad rows around  curves - powerful seeding of track candidates Conformal space C. Cheshkov

14. Other time performance improvements • Reduction of parameter space histograms size - 2 bytes per bin • Extensive usage of LUTs – param. space slopes and offsets for each pad • Dynamic pointers between neighbor track candidates – fast “jumping” during the parameter space filling • Fast parameterized calculation of pseudo-rapidity index C. Cheshkov

15. Tracking Performance • The presented tracking performance obtained with the following Hough space parameters: • Binning: 80(1)x120(2)x100() ~2x pad size in  direction • Range: tracking with minimum Pt = 0.5GeV/c • Chosen Hough space is a compromise between tracking efficiency, resolution and required computing time • Resolution ~ bin size • Comp. time ~ 1/bin size • Comp. time ~ 1/Ptmin C. Cheshkov

16. Hough transform tracking TPC sector – one  bin Parameter space • Track candidates are identified by a simple peak finder • Track parameters - at peak center • Track parameter cov. matrix: • Track parameter errors – fixed fraction of param. space bin size • Non-diagonal elements fixed to 0 – remove vertex constraint C. Cheshkov

17. Tracking efficiency • Tracking efficiency  95% • No dependence on event multiplicity • Sources of inefficiencies: • Binning (straight track assumption) • Track overlapping in the parameter space • Mult.scat. + energy losses C. Cheshkov

18. Resolution • Pt resolution dominated by param. space bin size: (1/Pt)~bin size  Pt/Pt=(Ahough*Pt + Bmult.scat) • No significant dependence on event multiplicity C. Cheshkov

19. Overall computing time for Hough Transform tracking • For comparison: Computing time ~ time needed just to unpack Huffman encoded TPC data • Only ~5% of the time is outside param. space filling C. Cheshkov

20. Conclusions • Tracking efficiency >95% and stable up to dN/dy~8000 • Fake track probability <2% up to dN/dy=4000 • Pt resolution rises linearly with Pt • About 5s comp. time for central PbPb event with dN/dy~4000 ~8 Mbytes/s processing rate (compressed data) ~0.15 s/ADC count (hit) • Time vs. resolution compromise by optimal param. space binning • FPGA implementation is under development - would allow to diminish the computing time to hundreds of milliseconds • Hough Transform tracks can be efficiently propagated to ITS • Possibilities for jet and open charm triggers look very promising C. Cheshkov