Fast Hough Transform Tracking for the ALICE TPC

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Fast Hough Transform Trackingfor the ALICE TPC

• C. Cheshkov
• 3-7 Oct 2005
• TIME05

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• 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

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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

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ALICE Detector Layout
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ALICE High Level Trigger

• Data rate from central PbPb collisions
  (dN/dy2000-4000)
• 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

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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

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ALICE TPC

• Outer and inner radii 84 cm and 250 cm
• Long. Size 5 m
• Acceptance ?lt0.9
• 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
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Central PbPb event (dN/dy6000)
Only primary tracks with Ptgt1GeV/c are shown
15-30 occupancy 50 million ADC amplitudes 3
million clusters 10000 tracks in the
acceptance 50 Mbytes compressed data
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ALICE HLT algorithms for TPC tracking

• Low multiplicity (up to dN/dy2000-3000)
• Cluster finder track follower (in Conformal
  Mapper space)
• 13s for dN/dy4000 (including 4s for cluster
  finder)
• Cluster finder implemented on FPGA
• High multiplicity (up to dN/dy8000)
• 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

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Hough Transform TPC tracking

• Hough Transform
• Highly parallelizable FPGA implementation
• Computing time - massive random memory access
• Efficiency and resolution limitations parameter
  space binning

Image space TPC sector

• 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

Parameter space
Track curvature
Emission angle
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Hough Transform TPC tracking
Pad rows
Pads

• Grayscale HT
• Parameter space histogram incremented by raw ADC
  counts
• Parameter space bins accumulate the charge along
  the track trajectory
• Peaks chargegtthreshold

• 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 gapsltthreshold

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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

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Parameter Space Definition
TPC sector layout

• Conformal Mapping space
• (x,y) ? ?x/(x2y2) , ?y/(x2y2)
• 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
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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

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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

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Hough transform tracking
Parameter space
TPC sector one ? bin

• 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

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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

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Resolution

• Pt resolution dominated by param. space bin size
• ?(1/Pt)bin size ? ?Pt/Pt(AhoughPt
  Bmult.scat)
• No significant dependence on event multiplicity

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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

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Conclusions

• Tracking efficiency gt95 and stable up to
  dN/dy8000
• Fake track probability lt2 up to dN/dy4000
• Pt resolution rises linearly with Pt
• About 5s comp. time for central PbPb event with
  dN/dy4000
• 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