Deep convolutional neural networks applied to muon tomography images Lara Lloret & Pablo Martínez Ruiz del Árbol October 2019 1st COMCHA school st 1 COMCHA School 2 http://www.cosmic-ray.org/reading/flyseye.html#SEC10 particles (1.8%) and others (< 0.2%) others and (1.8%) particles α TeV (1991, several since then) TeV 8 Cosmic rays are the most energetic particle ever seen so far. seen ever particle the energetic most are rays Cosmic Constant flux of high energy particles bombarding the Earth space. from the the Earth bombarding particles energy of high flux Constant (98%), protons by mainly Composed ➔ ➔ ➔ Cosmic rays: composition, flux, energy spectrum. Deep convolutional neuralnetworks applied muon tomographyto images The Oh-My-God Particle 3x10 st 1 COMCHA School 3 )(angle with vertical). the θ ( 2 whenintegrating solid angle. 3 3 GeV Rule of thumb the surface: at thumb of Rule and muonsminute. per squared meter 10000 Quicklyspectrafalling → average of Muonsare generated mostly from piondecays in atmosphere. the The fluxmuonsof is mostly proportionalcosto ➔ ➔ ➔ Cosmic muons:flux andenergy spectrum. Deep convolutional neuralnetworks applied muon tomographyto images 1 s t C O M Muon interaction with matter: ionization C H A S c h ➔ o Ionization is one of the most frequent processes for cosmic muons. o l ➔ Energy loss depends on the Z, density, and size of the crossed object. ➔ The Range is the distance for which the particle looses all the energy. Mean excitation potential Muon Energy/GeV Material Range/m 1 Water 471 10 Water 4260 1 Concrete 228 10 Concrete 2025 1 Standard Rock 209 10 Standard Rock 1857 Deep convolutional neural networks applied to muon tomography images 4 1 s t C O M Muons interaction with matter: multiple scattering C H A S c h ➔ o Coulomb scattering deviates the direction of muons when crossing matter. o l ➔ Scattering angle depends also on the Z, density, and size of the material. ➔ Angular distribution is approximately gaussian (with some tails). Momentum dependence Muon Material Width/cm Angle/mrad Energy/GeV 1 Iron 1 10 10 Iron 1 1 1 Iron 10 34 10 Iron 10 3 1 Lead 1 19 10 Lead 1 2 1 Lead 10 64 10 Lead 10 6 1 Uranium 1 26 10 Uranium 1 3 1 Uranium 10 88 10 Uranium 10 9 Deep convolutional neural networks applied to muon tomography images 5 1 s t C O M Two categories on muography applications C H A S c Absorption Muography Scattering Muography h o o l ➔ Muon flux measured as a function of the direction. ➔ Scattering position and angular shift. ➔ Differential transmittance “T”. ➔ Smaller Masses + shorter exposure times. ➔ Need Large Masses + Long exposure times. ➔ Applications: security, industry, etc. ➔ Applications: vulcanology, geology, archeology… ➔ At least two detectors are needed. ➔ Only one detector needed. Muon Detector T θ Δθ Δθ Muon Detector Muon Detector Deep convolutional neural networks applied to muon tomography images 6 1 s t C O M Two categories on muography applications C H A S c Absorption Muography Scattering Muography h o o l ➔ Muon flux measured as a function of the direction. ➔ Scattering position and angular shift. ➔ Differential transmittance “T”. ➔ Smaller Masses + shorter exposure times. ➔ Need Large Masses + Long exposure times. ➔ Applications: security, industry, etc. ➔ Applications: vulcanology, geology, archeology… ➔ At least two detectors are needed. ➔ Only one detector needed. Muon Detector T θ Δθ Δθ Muon Detector Muon Detector Deep convolutional neural networks applied to muon tomography images 7 1 s t C O M Muon detectors: gas proportional chambers C H A S c h Chamber 1 o o l X measurement Y measurement Chamber 2 Surface: 1m x 1m N. wires: 212 Synch Wire: Gold-Tungsten + Wire radius: 25 μm Trigger Chamber 3 Synchronization Gas: Ar-CO2 electronics Chamber 4 Deep convolutional neural networks applied to muon tomography images 8 st 1 COMCHA School 9 Muon detectors: gas proportional chambers Deep convolutional neuralnetworks applied muon tomographyto images 1 s t C O M Image reconstruction in muon tomography C H A S c ➔ h Tomography is a classic “inverse” mathematical problem. o o l ⃗x Input variables for a given dynamical system Example: Position/direction of a muon at the upper detector. ⃗f Physics laws: evolution of the system. Notice: Can be deterministic but also probabilistic. ⃗y=⃗f (⃗x ;θ⃗) Example: Moliere’s scattering formula for angular deviations. θ⃗ Parameters describing the physics environment. Example: Densities and geometry of the crossed material. ⃗y Output variables after the action of ⃗f . Example: Position/direction of a muon at the lower detector. Deep convolutional neural networks applied to muon tomography images 10 1 s t C O M Image reconstruction in muon tomography C H A S c ➔ h Tomography is a classic “inverse” mathematical problem. o o Given l ⃗x Input variables for a given dynamical system Example: Position/direction of a muon at the upper detector. Known ⃗f Physics laws: evolution of the system. Notice: Can be deterministic but also probabilistic. ⃗y=⃗f (⃗x ;θ⃗) Example: Moliere’s scattering formula for angular deviations. Known θ⃗ Parameters describing the physics environment. Example: Densities and geometry of the crossed material. Unknown ⃗y Output variables after the action of ⃗f . Direct problem Example: Position/direction of a muon at the lower detector. Deep convolutional neural networks applied to muon tomography images 11 1 s t C O M Image reconstruction in muon tomography C H A S c ➔ h Tomography is a classic “inverse” mathematical problem. o o Given l ⃗x Input variables for a given dynamical system Example: Position/direction of a muon at the upper detector. Known ⃗f Physics laws: evolution of the system. Notice: Can be deterministic but also probabilistic. ⃗y=⃗f (⃗x ;θ⃗) Example: Moliere’s scattering formula for angular deviations. Unknown θ⃗ Parameters describing the physics environment. Example: Densities and geometry of the crossed material. Known ⃗y Output variables after the action of ⃗f . Inverse problem Example: Position/direction of a muon at the lower detector. Deep convolutional neural networks applied to muon tomography images 12 1st COMCHA School 13 pproach (POCA) pproach A losest losest C int of Po Works very well for scenarios that are essentially empty with some high density chunks. density high some with empty essentially are that for scenarios well very Works The scattering occurs only at one point during the whole trajectory. trajectory. whole the during point at one only occurs The scattering The simple geometric approach: POCA ➔ ➔ Thiscomplex problem can be approximated doingsome physicalassumptions ➔ Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 14 The simple geometric approach: POCA Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 15 wear Side view wear Top view Top Front view wear The simple geometric approach: POCA Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 16 50 cm 20 cm 20 cm R 20 cm 24.06 cm 24 cm Aluminium Steel wool Rock Measurement ofthe width ofan insulated pipe DOI:10.1098/rsta.2018.0054 Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 17 50 cm 20 cm 20 cm R 20 cm 24.06 cm 24 cm Aluminium Steel wool Rock Measurement ofthe width ofan insulated pipe DOI:10.1098/rsta.2018.0054 Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 18 50 cm 20 cm 20 cm R 20 cm 24.06 cm 24 cm Aluminium Steel wool Rock Measurement ofthe width ofan insulated pipe DOI:10.1098/rsta.2018.0054 Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 19 50 cm 20 cm 20 cm R 20 cm 24.06 cm 24 cm Aluminium Steel wool Rock Measurement ofthe width ofan insulated pipe DOI:10.1098/rsta.2018.0054 Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 20 Measurement ofthe width ofan insulated pipe About 1 hour of data taking. of data hour 1 About Assuming perfect resolution. perfect Assuming Geant4 + local chamber response. +chamber Geant4 local CRY (*) generator. (*) CRY Simulation Details: Simulation https://nuclear.llnl.gov/simulation/doc_cry_v1.7/cry.pdf Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 21 Thickness = 2.6 cm Thickness Thickness = 1.8 cm Thickness Thickness Thickness = cm 1.6 Thickness = 2.4 cm Thickness Thickness = 1.2 cm Thickness Thickness = 2.0 cm Thickness Reconstructedwidths images fordifferent Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 22 Thickness = 2.6 cm Thickness Thickness = Thickness cm 1.8 Thickness = 1.6 cm Thickness Thickness = 2.4 Thickness cm Thickness = cm 2.0 Thickness Thickness = 1.2 cm Thickness Simulations with realistic detector Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 23 Thickness = 2.6 cm Thickness Thickness = Thickness cm 1.8 Thickness = 1.6 cm Thickness Thickness = 2.4 Thickness cm QUESTION: Thickness = cm 2.0 Thickness Thickness = 1.2 cm Thickness How to quantify and discern the thickness of the pipes? Simulations with realistic detector Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 24 A CNN isnetwork a filtersof operating over sub-spaces of input. the A Imagesare 2x1 dimensiontensors: horizontal-verticalpixel x color/depth. CNNare MachineLearning algorithms designed operateto with images. Convolutional neural networks (briefreminder) ➔ ➔ ➔ Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 25 Multiplying and = 0 adding Multiplying Multiplying and = (50*30) adding + (50*30) +Multiplying (50*30) + (20*30)+(50*30) = 6600 Filtersoperating onaparticular sub-space produce a single number. Convolutional neural networks (briefreminder) ➔ Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 26 Features map Features Filter 5x5 Filter Asthespans filter wholethe tensorinitial producesit anew “image”. Convolutional neural networks (briefreminder) ➔ Deep convolutional neuralnetworks applied muon tomographyto images 1st COMCHA School 27 Denselayers arenormal NNlayers useful specially thein last stages.