Maximum Likelihood Estimation Maximization
for NEXT event reconstruction
Christoph Lerche, Alexander Izmaylov, Paola Ferrario,
Ander Simon, Juan Jose Gomez-Cadenas, Francesc Monrabal
NEXT Event reconstruction challenges
Anode
SiPMs plane
EL
region
Cathode
PMTs
•  Primary scintillation light gives T0 signal
•  Ionization in Xe gas ! electrons propagate to EL region to give secondary
scintillation detected by cathode (PMTs, energy) and anode (SiPMs, position)
•  Observed signal is a primary energy deposit affected by diffusion (longitudinal +
transverse) + charge loss (attachment) + EL light creation + reflections + sensor
efficiency + noise
•  In order to improve pattern reconstruction/energy resolution need to de-convolute
the effects ! solve the “inverse” problem
•  Since track is mostly dominated by random walk it is more image reconstruction
than tracking (aka kinematic params estimation)
2
Image reconstruction problem
•  The problem arises in many areas
•  Medical physics imaging , Positron Emission Tomography (PET)
•  Collinear photon counts ! body image
•  A number of approaches to solve the inverse problem ! try applying to NEXT
events " Maximum Likelihood Estimation Maximization
3
MLEM method for NEXT events
Iterative approach to solve the problem:
what is the E deposit in drift volume that
leads to detected pattern with max likelihood
* Lange and Carson, J Comp Ass Tomog, 1984
4
MLEM method for NEXT events, cont`d
Probability matrix
Detector data
Forward projection + noise
• 
Voxels in drift volume ! build a probability matrix to associate image bins with the ones of
detector planes
• 
MC derived matrix for EL bins "! detector planes: light production, efficiencies
• 
Then able to convolute it with diffusion, loss due to attachment etc
• 
Implement charge cut to reject “zero” bins (voxels) to iterate faster
• 
Account for noise
• 
Can stop the iterations when current change to forward projection
(wrt to measured detector data) is below a given cut
5
MLEM method for NEXT events, imaging modes
2D & 2D+1
2D mode:
•  sum-up (collapse time) time-signals for
each-pixel
•  reconstruct “2D” projection ! pattern at
EL plane based on anode/cathode signals
•  simple and fast: can be used to do basic
checks of the method: is working etc
•  can account for light-propagation from EL
to anode/cathode
2D+1 mode:
•  deal with time-slices
•  for each time-slice solve 2D problem
•  rather simple and fast
•  can account for light propagation from EL
to cathode/anode and charge loss (~ exp
decrease based on Z due to attachment)
•  no full drift: not possible to account for
longitudinal dispersion + some EL light6
production features
MLEM method for NEXT events, imaging modes
Full 3D
Full 3D mode:
•  consider 3D image voxels (x,y,z) in drift volume
•  account for longitudinal dispersion and charge loss: probability of i-th Z pixel` photon to be
collected during time-slice j and charge decrease
•  can account for transverse dispersion by estimating the probability of a certain (Z,X)/(Z,Y)
pixel` photon to contribute to a particular X/Y pixel at EL plane
•  quite slow
7
Example: 2D+1 algorithm applied for NEXT Demo
1 MeV electrons in NEXT Demo
2D+1 imaging mode
2D XY projections shown
True info voxelized
MLEM reconstructed pattern
8
Anode signal
Current status
•  Preliminary tests with 2D and 2D+1 modes
•  Understanding of 3D/partial 3D
•  Algorithm tuning: convergence criteria, charge cuts …
•  3D is quite slow ! need to think of parallelizing processing (a
common approach in medical physics):
NEXT Demo iteration: 2D (~100 msec) x ~150 (2D+1) x ~150 (3D)
9
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