Augmented Signal Processing in Liquid Argon Time Projection Chambers with a Deep Neural Network
Haiwang Yu, Mary Bishai, Wenqiang Gu, Meifeng Lin, Xin Qian, Yihui Ren, Andrea Scarpelli, Brett Viren, Hanyu Wei, Hongzhao Yu, Kwang Min Yu, Chao Zhang
PPrepared for submission to JINST
Augmented Signal Processing in Liquid Argon TimeProjection Chambers with a Deep Neural Network
H. W. Yu, a , M. Bishai, a W. Q. Gu, a M. F. Lin, b X. Qian, a Y. H. Ren, b A. Scarpelli, a B. Viren, a H. Y. Wei, a H. Z. Yu, c K. Yu, b C. Zhang a a Physics Department, Brookhaven National Laboratory, Upton, NY, USA b Computational Science Initiative, Brookhaven National Laboratory, Upton, NY, USA c Sun Yat-Sen (Zhongshan) University, Guangzhou, China
E-mail: [email protected]
Abstract: The Liquid Argon Time Projection Chamber (LArTPC) is an advanced neutrino detectortechnology widely used in recent and upcoming accelerator neutrino experiments. It features a lowenergy threshold and high spatial resolution that allow for comprehensive reconstruction of eventtopology. In current-generation LArTPCs, the recorded data consist of digitized waveforms onwires produced by induced signal of drifting ionization electrons, which can also be viewed as two-dimensional (2D) (time versus wire) projection images of charged-particle trajectories. For suchan imaging detector, one critical step is the signal processing that reconstructs the original chargeprojections from the recorded 2D images. For the first time, we introduce a deep neural network inLArTPC signal processing to improve the signal region of interest detection. By combining domainknowledge (e.g., matching information from multiple wire planes) and deep learning, this methodshows significant improvements over traditional methods. This work details the method, softwaretools, and performance evaluated with realistic detector simulation.Keywords: LArTPC, Signal Processing, Wire-Cell, Deep Neural Network Corresponding author a r X i v : . [ phy s i c s . i n s - d e t ] A ug ontents The Liquid Argon Time Projection Chamber (LArTPC) is a key detector technology for manycurrent and anticipated future accelerator neutrino experiments [1–4]. When charged particlestransverse through the LAr medium, both scintillation light and ionization electrons are created.While the detection of scintillation light provides the event time, the detection of ionization electronsaffords high-resolution position and energy information about particle trajectories. The rich eventtopology information provided by LArTPC offers unique advantages in performing electron-photonseparation. Together with superior calorimetry capability, LArTPC is an excellent detector to study ν µ to ν e oscillations, which may hold the key to answering some remaining questions in the neutrinosector [5].The current-generation LArTPCs are typically equipped with wire readouts, instead of pixelatedreadouts that is being developed rapidly [6], under the consideration of cost and heat production ofelectronics inside LAr [7]. In this configuration, the anode typically consists of multiple (commonlythree) wire planes with different wire orientations. Under a uniform external electric field, theproduced ionization electrons drift toward the anode planes at a (known) constant speed. Thearrival time of ionization electrons, combined with the event time provided by the light detectionsystem, allows for a position reconstruction of activities along the electric field. The combinationof wire signals from different planes provides the position information perpendicular to the electricfield. Together, three-dimensional (3D) reconstruction of activities inside LArTPC can be made.To realize this concept, wire planes with different orientations must record signals from the sameionization electron cloud multiple times. This is achieved using both induction and collection wire– 1 –lanes. By properly configuring the electric fields between wire planes, the ionization electronscan fully pass through the first few (induction) wire planes then get collected by the last (collection)wire plane. When ionization electrons move close to the wires, induced current can be detected.As governed by Ramo’s theorem [8], the induced current has bipolar and unipolar shapes onthe induction-plane and collection-plane wires, respectively. While signal reconstruction for thecollection-plane wires is generally simpler, it is more complex for the induction-plane wires giventhe potential large cancellation effect of the bipolar signals. In this work, we introduce a novelsignal processing procedure utilizing modern deep learning techniques and assisted by correlatinginformation from multiple planes. This new procedure leads to an improved reconstruction ofionization electron distributions, which further enhances the quality of overall event reconstruction.The recorded digitized TPC signal is a convolution of the distribution of the arriving ionizationelectrons and the impulse detector response: M ( t , x ) = ∫ ∞−∞ ∫ ∞−∞ R ( t − t (cid:48) , x − x (cid:48) ) · S ( t (cid:48) , x (cid:48) ) dt (cid:48) dx (cid:48) + N ( t , x ) , (1.1)where M ( t , x ) is a measurement, such as an Analog to Digital Converter (ADC) value at a givensampling time and wire position; R ( t − t (cid:48) , x − x (cid:48) ) is the impulse detector response, including both thefield response that describes the induced current by a moving ionization electron and the electronicsresponse from the shaping circuit; S ( t (cid:48) , x (cid:48) ) is the charge distribution in time and space of the arrivingionization electrons; and N ( t , x ) is the electronics noise. The goal of TPC signal processing is toreconstruct the original charge distribution S from the measurement M given the known detectorresponse R in the presence of the electronics noise N .Developed from earlier work in ref. [9], the current state-of-the-art algorithm to reconstructthe original ionization electron distribution is the so-called “2D deconvolution” technique [10, 11]using Discrete Fourier Transformation. This TPC signal processing algorithm is implemented inthe Wire-Cell
Toolkit [12] and can be run as a plug-in of the LArSoft software suite [13]. Althoughthis algorithm has shown good performance and has been adopted in many experiments, there isstill room to improve, especially for large angle tracks with respect to the wire orientation. Thesetracks are known as the “prolonged tracks” because they induce current on a given wire over anextended period of time [10]. Figure 1 illustrates the challenge in signal processing for prolongedtracks (with an 80°track angle). In this work, the track angle is defined by the track projection on a2D plane, where the x-axis is the wire pitch direction and y-axis is the electron drifting direction.The track angle is measured by the angle between track projection and the x-axis in this plane,defined as θ xz . This angle definition is the same as that used in figure 8 of ref. [10].While the TPC signals for a track with a θ xz =
45° are clear (see. figure 1), the ones for a trackwith θ xz =
80° are rather weak. Such a big difference with respect to the track angle is the result ofthe bipolar and long-range nature of the induced current for a point source on the induction-planewires. Thus a prolonged track leads to large cancellation of the induced current, resulting in a lowsignal-to-background ratio. The same conclusion can be drawn when viewing from the frequencydomain. First, the average response function of the induction-plane wires must approach to zeroat low frequency (e.g., figure 12 of [10]) as the net charge collected on an induction-plane wire iszero [8]. Second, the signal of a prolonged track mostly resides at low frequency. Therefore, themeasured signal strength, which is the product of signal strength from a prolonged track and the– 2 –
Figure 1 : Left: projection of a minimum ionizing particle (MIP) track on one induction plane;right: a section of waveform of wire 1120 from the left plot indicated by the dashed box. Trackangle projected on this plane is 45° (Top) and 80° (Bottom) with respect to the wire orientation.The recorded signal for the 80° track is weak as the result of the cancellation effect of the bipolarfield response and the extended (in time) distribution of ionization electrons.average response function, can become small compared with the low-frequency electronics noise,leading to a poor signal-to-noise ratio. To achieve good performance of the signal processing,ref. [10] introduced a region of interest (ROI) detection technique, whose goal is to define anROI in the time domain to contain the distribution of ionization electrons. The ROI significantlyreduces low-frequency noise for the induction planes, which, in turn, increases the signal-to-noiseratio. Obviously, to maximize the signal-to-noise ratio, the ROI fully containing the distribution ofionization electrons in the time domain should be as small as possible. For this reason, the ROIfinding algorithm in ref. [10] worked on the deconvolved waveform instead of the raw waveformbecause the ROI found in the latter case is typically bigger as a consequence of the extended– 3 –etector response. With a set of heuristic logic, the ROI searching algorithm in ref. [10] furtherutilizes the connectivity information of ROIs on adjacent wires in a wire plane to enhance ROIdetection efficiency as the TPC signals tend to be continuous for any charged particle track. Ofnote, while the ROI detection is crucial for induction-plane signal processing, it is less importantfor collection-plane signals, where the field response is generally unipolar.However, even with the usage of “2D deconvolution” technique and “connectivity” information,some TPC signals, e.g. prolonged tracks, are still hard to identify. Adding more informationprogressively into the heuristic logic of the ROI detection algorithm [10] is not a scalable approach.Hence, we propose a novel LArTPC signal processing procedure based on the Deep Neural Network(DNN). DNNs are known to manage complicated correlations and cover solution phase space moreefficiently. In the field of high energy physics, there are many successful applications of DNNs (seerefs. [14–18], among others). Furthermore, inspired by the
Wire-Cell imaging concept in ref. [19],the TPC signals from other wire planes can enhance ROI detection efficiency by using the geometryinformation from multiple wire planes. Combining machine learning and domain knowledge, thenew DNN LArTPC signal processing shows significantly improved performance, especially forprolonged tracks.This paper is organized as follows: section 2 briefly reviews the current state-of-the-art signalprocessing, and section 3 introduces the new DNN signal processing. The DNN architecture,
Wire-Cell imaging concept, simulation and data pre-processing, and network training are describedin sections 3.1, 3.2, 3.3, and 3.4, respectively. The DNN signal processing performance evaluationis presented in section 4 followed by the section 5 summary.
As introduced in section 1, LArTPC signal processing extracts ionization charge distribution as afunction of drift time and wire number from the induced current on the readout wires. Figure 2shows a simplified flowchart of the state-of-the-art signal processing algorithm in Refs. [10, 11].
Decon. w/ Tight LFDecon. w/ Loose LF
ROI Detection
ROI
2D decon.
Data after Noise Filtering Decon. for Charge Charge
Figure 2 : Flowchart of the LArTPC signal processing algorithm in ref. [10]. “LF” stands forlow-frequency software filter, while “decon.” denotes deconvolution.Starting from the noise-filtered waveform [20], several 2D deconvolutions are performed withdifferent software filters in the frequency domain. Each deconvolution follows Eq. 2.1, resolvingthe signal S using measurement M and detector response R in the frequency domain. A follow-upInverse Fourier Transform ( I FT ) converts the signal S back to the time and space domain. Softwarefilters ( F ) in the frequency domain are used to suppress noise at high and/or low frequencies. Here,the low-frequency filter is necessary (not used) to process signals in the induction-plane (collection-– 4 –lane) wires as the bipolar nature of induction-plane wires’ field response suppresses signals atlow frequency. The different low-frequency filters have distinct features in the signal extraction.For example, a tight low-frequency filter limiting the bandwidth at a higher frequency value leadsto a high-purity but low-efficiency signal extraction. On the other hand, a loose low-frequencyfilter expanding the bandwidth to lower frequency results in a low-purity but high-efficiency signalextraction. S ( ω t , ω x ) ∼ F ( ω t , ω x ) · M ( ω t , ω x ) R ( ω t , ω x ) I FT −−−−−−−→ S ( t , x ) . (2.1)With the deconvolved waveform, ROI detection is performed to identify signal regions that aremore likely caused by ionization signals (instead of noise). The ROI detection step intends toopen windows just large enough to contain signals and maximize the signal-to-noise ratio. Aset of heuristic logic is implemented to detect ROIs from the deconvolved signals with loose andtight low-frequency filters based on the connectivity information. With the ROI windows defined,the waveforms outside are suppressed to zero, which reduces data size significantly and makesthe reconstruction steps that follow computationally more efficient. The detected ROIs are thenapplied on the deconvolved waveform without applying low-frequency filters ("Decon. for Charge"in figure 2). While removing the low-frequency filters minimizes the distortion on the ionizationelectron distribution, applying ROIs in the time domain keeps the signal-to-noise ratio high, whichis necessary for induction-plane wires.The goal of ROI detection is to achieve high efficiency and high purity. This can be challengingwhen the signal-to-noise ratio is low, such as with the prolonged tracks described in section 1. Inaddition, the heuristic logic in ROI detection sometimes may fail in a busy situation where numerousactivities are present (e.g., near neutrino interaction vertex or inside an electromagnetic shower).Section 3 introduces a novel ROI detection algorithm using a convolutional neural network basedon information from multiple wire planes, which notably improves signal processing performance. In this section, we describe the details the Deep Neural Network (DNN) architecture, use ofgeometric information from multiple wire planes, the simulation and data pre-processing, and thenetwork training.
To apply the DNN, the ROI detection problem is essentially labeling each pixel in a 2D image(with one dimension spanning LArTPC readout channels and the other drift time) as “signal”or “not-signal” (noise). Such a problem of dividing pixels from a picture into separated groupsbelongs to the class of machine learning procedures called semantic segmentation . We adoptedthe U-Net network architecture, introduced by O. Ronneberger et al. [21] in 2015, which has beendeveloped into a family of network architectures (see Refs [17, 22], among others). Figure 3 showsthe network configuration, which consists of an initial encoding path, a final decoding path, and– 5 –kip connections which bridge these first two paths at various levels. Each level contains two3 × × ( = × ) ×
48 pixels.
In a LArTPC with multiple wire planes, each ionization electron is independently sensed by eachwire plane. Therefore, information from the other wire planes can be used to assist ROI detection inthe targeted wire plane by correlating the geometric relation among wires with different orientations.Such geometric constraints are expected to be more efficient for LArTPCs with three or more wireplanes. For example, we use a three-plane configuration with the first two induction planes, labeledas “U” and “V”, and the final collection plane, denoted as “W”. This idea of multi-plane constraint insignal processing is inspired by the
Wire-Cell tomographic reconstruction technique from ref. [19].The procedure for implementing geometric constraints on the induction-plane wires is describedbelow and illustrated in figure 4:1. For each channel, initial signal ROIs are formed by combining the deconvolved signals withtight and loose low-frequency software filters (see figure 2). The combination uses theconnectivity information but skips the majority of heuristic logic in refining ROIs.2. Across the channels, these initial signal ROIs are sliced into contemporaneous time slicesof fixed duration (e.g., four time ticks or two µ s). This choice ensures negligible loss ofinformation following the Nyquist sampling theorem.3. In a given time slice, we determine a subset of channels from each plane consisting of thosethat are inside the initial signal ROIs.4. For each induction-plane channel inside the subset, we determine if any of its wires overlapwith two wires from the other two subsets (one from each). ∗ The successfully matchedchannels are referred to as the three-plane coincidence (MP3).5. For each induction-plane channel outside of the subset, we determine if any of its wiresoverlap with two wires from the other two subsets (one from each). The successfully matchedchannels are referred to as the two-plane coincidence (MP2).6. Steps 3 to 5 are repeated for every time slice. ∗ In the case of wrapped wires, one channel may correspond to multiple wires. – 6 –
BN, ReLU Max Pool, 2×2conv. 3×3 Up sampling, pad copy and cropout conv. input: waveform frame output: tagged ROIa b c
Figure 3 : U-Net architecture used in the ROI detection for the DNN LArTPC signal processing.Intermediate 2D images are generated from original images containing the raw waveform. Severalof these intermediate images are stacked to a multi-channel 2D image serving as the U-Net input.Numbers of intermediate images can vary. In this example, three are used: a) deconvolved signalsfrom a loose low-frequency filter, b) MP2, and c) MP3. Output of the U-Net is a single channel 2Dimage labeling each pixel as signal (i.e., inside ROI) or not.Identifying the coincidence (MP2 or MP3) is a combinatorial problem with the potential to requireprohibitive computational expense. To combat this, we developed an optimization technique for theprimitive operations used to determine wire overlap by exploiting the symmetries of uniform wiredirection and pitch. More details can be found in appendix A.As shown in figure 3, three 2D images are used as input to the DNN to detect the ROI foreach induction wire plane. The first image is the deconvolved result after applying the loose low-frequency software filter. The content in each 2D pixel (one channel and one time tick) is a floatnumber representing the reconstructed ionization charge. The second image is the result of MP2.The content in each pixel is a number with the Boolean type and unity (zero) labeling the pixel to– 7 –e inside (outside) the MP2. The last image is the result of MP3 also with Boolean type. AlthoughMP2 and MP3 are obtained after rebinning four time ticks into one time slice, it is straightforwardto determine if one pixel with one time tick is inside the MP2 or MP3 region. Figure 5 depicts anexample of these arrays.
1: make time slices2: Matching active wires (with initial ROI) from multiple planes 3: On target plane, tag 3-plane matched ROIs (MP3) or 2-plane matched ROIs (MP2)MP3 active wire in the time-slice :ref. plane, target planein-active wire in the time-slice
MP2U V Wchannel channel channel t i m e Figure 4 : Illustration of creating MP2 and MP3 images. The application of geometric constraintsis performed at each time slice (four time ticks).
The data samples used to train the network are generated from a comprehensive and detailedsimulation over multiple stages of physics. These begin with an initial sampling of kinematicsfrom cosmic ray muon models [23]; particle passage through detector material and the resultingenergy depositions [24]; the production of electrons, including recombination effects [13]; anddetector signal and noise simulation [12]. The detector response in the last step is provided bythe
Wire-Cell
Toolkit that includes ionization electron drift, diffusion, stochastic fluctuations, fieldresponse, and electronics response. The data pre-processing steps include excess noise filtering,initial deconvolution, and initial ROI finding. Excess noise filtering is particularly crucial in dealingwith real detector data, but it is less important for simulation. The initial deconvolution and ROIfinding are discussed in section 3.2 and more details can be found in ref. [25]. The simulation anddata pre-processing chain is validated with the ProtoDUNE Single Phase detector (described inref. [26]). – 8 –he input to DNN consists of MP2 (figure 5c), MP3 (figure 5d), and deconvolved signals froma loose low-frequency filter (figure 5b). Notably, MP2 and MP3 are generated from the deconvolvedsignals with tight (figure 5a) and loose low-frequency filters. For each event sample, there are atotal of 6000 time ticks covering 3 ms drift time. The number of channels are 800, 800, and 960for induction U, induction V, and collection W planes, respectively. The average number of cosmictracks is about 11 per event. To limit memory use, 10 time ticks are rebinned into one time bin,which limits the typical data size of the induction plane to 600 time bins and 800 channels. For any2D image, the content value in each rebinned pixel is taken as the average of the original value in 10pixels (e.g., number of electrons for the deconvolved signal and 0 or 1 for MP2 and MP3). While thenumber of ticks used in this rebinning process could be further optimized, such a rebinning choicehas minimal impact on the ROI detection because a majority of the ROIs ( > truth label is created by applying asimple ideal-detector model to the initial simulated ionization electron distributions (a smearingwith Gaussian distribution). A threshold is applied on the charge of a rebinned pixel (one channeland one time bin covering 10 time ticks) to determined if a rebinned pixel contributes to an ROI.In particular, the threshold is chosen to be 100 electrons on the average charge per time tick in arebinned pixel. This value is much lower than the equivalent noise charge (ENC) from the entireelectronics readout chain, which typically exceeds 400 electrons per time tick. The average numberof (true) ROIs in an induction plane is about 3500 per event. Figure 5(e) shows an example of thetruth label. The network and supporting utilities are implemented using PyTorch [27] and are publiclyaccessible in ref. [28]. We trained the network on a platform with Intel i9-9900K CPU and NVIDIA2080 Ti GPU with 11 GB VRAM [29]. A training epoch consists of a total of 500 event samples(450 for training and 50 for validation) and requires six minutes on this platform. Each sampleconsists of one tensor holding the binary “signal”/“not-signal” truth label elements and a secondtensor holding three 2D arrays (deconvolved signal with loose low-frequency filter, MP2, and MP3).With the cosmic ray simulation, each sample contains about 5 to 20 cosmic rays, resulting in anaverage of 3500 ROIs per sample. We use binary cross-entropy [30] as the loss function andstochastic gradient decent [31] with momentum 0.9 and learning rate 0.1 as the optimizer. In thenext section, performance of this DNN ROI detection is evaluated.
The performance of the trained network with simulation is initially evaluated by focusing on themore challenging cases of the ideal (large-angle) prolonged tracks. For each 3D track, two projectionangles, θ xz ( V ) and θ xz ( U ) with respect to V and U wire planes, are used to described its 3D direction.A larger projection angle with respect to a wire plane means a longer ROI in time, which is morechallenging to detect. Two metrics are used to evaluate the performance with the rebinned pixels.Pixel-wise (rebinned) efficiency is defined as: – 9 – )b) c)d) e) Figure 5 : Example neural network input channels obtained from cosmic ray simulation for aninduction wire plane: a) deconvolved image with a tight low-frequency filter; b) deconvolved imagewith a loose low frequency filter; c) multi-plane 2-plane coincidence (MP2); d) multi-plane 3-planecoincidence (MP3); and e) truth information. Here, the deconvolved images with tight and looselow-frequency filters from different wire planes are used to produce the MP2 and MP3 images. Thedisplayed images feature original binning of 6000 time ticks and 800 channels. A prolonged trackis indicated by the black rectangle dashed line. The input to DNN consists of b), c), and d).Pixel Efficiency : = . (4.1)Pixel-wise purity is defined as:Pixel Purity : = . (4.2)In this evaluation, induction V wire plane is used as an example. Figure 6 compares pixel-wise ROI detection efficiency and purity for three algorithms: 1) current state-of-the-art ROIdetection algorithm from ref. [25] as the reference, 2) DNN ROI detection without the multi-planegeometry information, and 3) DNN ROI detection with the multi-plane geometry information. Clearimprovements can be gleaned from the DNN ROI detection algorithm:1. The DNN ROI detection algorithm outperforms the reference algorithm, especially for ex-treme large-angle tracks ( >
75, 75 80, 80 82, 82 85, 85 87, 75 87, 85 87, 87 xz ( V ), xz ( U )0.00.20.40.60.81.01.21.4 P i x e l E ff i c i e n c y Ref.DNN without MPDNN with MP 75, 75 80, 80 82, 82 85, 85 87, 75 87, 85 87, 87 xz ( V ), xz ( U )0.00.20.40.60.81.01.21.4 P i x e l P u r i t y Ref.DNN without MPDNN with MP
Figure 6 : Pixel-wise (rebinned) ROI detection efficiency and purity for three ROI detection algo-rithms evaluated using simulated prolonged tracks. X-axis is track projection angle on the respectiveinduction V and U planes in degrees. ROI detection is performed on the targeted induction V plane.Using various, reconstructed event images, figure 7 shows additional DNN ROI detection algorithm– 11 –mprovements. Row (1) of figure 7 shows the reconstructed images of simulated ideal tracks withprojection angles 87° on V plane and 85° on U plane for the three ROI detection algorithms (columnsb-d), as well as the truth label (column a). Improvements in terms of efficiency and purity numbers(shown in figure 6) are evident. Rows (2) and (3) in figure 7 show reconstructed images fromsimulations generated from charged pions overlaid with cosmic rays. While row (2) focuses on thereconstruction of a prolonged cosmic ray track, row (3) centers on a busy interaction region of acharged pion. The DNN ROI detection algorithm with multi-plane information, column (d), has thebest performance among all scenarios when compared with truth labels in column (a). The sameconclusion can be drawn when applying the DNN ROI detection algorithm on the ProtoDUNESingle Phase data [32]. Preliminary results can be found in ref. [33].In addition to U-Net, we also implemented and evaluated two other network structures: URe-stNet and Nested-U-Net. URestNet [17] is U-Net with residual connections. Nested-U-Net [22] isU-Net with dense skip connections. With proper optimizations in the training, all three networksperform similarly. U-Net uses slightly less ( ∼ Wire-Cell
Toolkit [12]. The trainedmodels are serialized in the TorchScript format. Table 1 shows a comparison of the inferencingtime, memory usage, and VRAM use among the three ROI detection algorithms.
Table 1 : Comparison of resource usage for three ROI detection algorithms. Reference is the currentROI detection algorithm from ref. [25]; DNN CPU/GPU: DNN ROI detection algorithm proposedin this paper, inferencing with CPU/GPU, respectively.Method Time per plane [sec] Memory [GB] VRAM [GB]Reference 0.40 1.3 -DNN CPU 16.7 4.8 -DNN GPU 0.14 3.7 3.7
For the first time, we have developed a novel DNN ROI detection algorithm for LArTPC signalprocessing. As described in this paper, we adopted the ProtoDUNE configuration in the exper-iment, but the generic idea and procedure should work on all types of projective wire readouts.The implementation in the
Wire-Cell
Toolkit utilizes the TorchScript APIs, which enables usingtrained PyTorch models in the C++ production environment. This algorithm takes advantage ofmodern machine learning techniques, as well as the domain knowledge specific to LArTPC signalprocessing (2-D deconvolution, multi-plane geometry correlation, etc.). Quantitative evaluationsshow this DNN ROI detection algorithm outperforms the current state-of-the-art ROI detectionalgorithm. Such improvement is expected to generate a better reconstruction of event topology ina LArTPC, particularly for detectors with higher noise and lower signal-to-noise ratio (e.g., withwarm electronics [3]). – 12 – a) (b) (c) (d)(1)(2)(3)
Figure 7 : Event display showing the detected ROIs on different types of event topologies: (1)Ideal straight-line prolonged tracks with track angle of 87° projected to V plane and 85° projectedto U plane, (2) cosmic track with a section featuring a large projection angle (indicated by theblack rectangle dashed line), and (3) an interaction vertex of a charged pion with many activities(indicated by the black rectangle dashed line). ROI detection is performed on the V plane (targetplane). The column labels are: (a) truth label, (b) reference ROI detection algorithm [25], (c) DNNROI detection algorithm without the multi-plane geometry information, and (d) DNN ROI detectionalgorithm with the multi-plane geometry information.
Acknowledgments
This work is supported by the U.S. Department of Energy, Office of Science, Office of High EnergyPhysics and Early Career Research Program under contract number DE-SC0012704. We thank theDUNE collaboration for use of its Monte Carlo simulation software and related tools. We wouldalso like to show our gratitude to Charity Plata (Computational Science Initiative of BrookhavenNational Laboratory) for her inputs during the manuscript preparation.– 13 –
Fast Projection using the Ray Grid Technique
Central to the use of geometry information for improving signal processing efficiency, as well as inthe
Wire-Cell
3D tomographic reconstruction technique [19], are a number of primitive operationsthat must be carried out numerous times by these higher-level algorithms. Optimization of thesefrequently called operations is critical for overall speed. Two core and related operations involvelocating the intersection point of a wire from each plane and then locating a wire from a third planerelative to this intersection. The so-called ray grid method is used to optimize these operations byexploiting two symmetries of an idealized wire plane: fixed wire pitch and direction. Exploitingthese symmetries transforms the problem from solving a vector equation to a simpler problem ofapplying indices. - - - - - - r w w ij01 r p p p ij012 p iw jw Figure 8 : Example points, vectors and tensors involved in constructing and using ray grids. Layers0, 1 and 2 are represented in red, blue and black, respectively. See text for further definitions.With these symmetries assumed, we start by generalizing a fixed number of parallel wires ina wire plane to an infinite number of parallel rays in a layer . This generalization allows us todefine the active area of an anode by introducing two logical layers, one providing horizontal andthe other providing vertical boundaries via rays with pitch equal to the active height and width,– 14 –espectively. The higher-level algorithms do not care about wires per se but about the logical linesrunning parallel to and halfway between two neighboring wires and in so in practice we associatethe abstract rays to these lines. Finally, as the higher-level algorithms work in a projected space, weassume all layers are co-planar, which allows the problem to reduce to two dimensions.A set of rays in a layer and their relationship to rays in a second or third layer may be categorizedby a number of tensors listed below and illustrated for a three layer problem in figure 8. Withinone layer we may consecutively number the rays and we mark these tensor indices with subscripts( ∈ { i , j , k } ). We identify a special ray with an index of zero. The precise identification does notmatter for the ray grid method. In practice the ray nearest to an edge of the active region is chosen.For quantities that span multiple layers, we mark them with superscript layer indices ( ∈ { l , m , n } ). p l the pitch vector for layer l gives the displacement perpendicular to the layer’s rays and hasmagnitude that of the pitch separation of two neighboring rays. c n the origin vector for layer n locates the center point of the specially identified ray i = r lmij the crossing point of ray i from layer l and ray j from layer m . r lm the crossing point the specially identified zero rays of layers l and m . w lm a vector giving the displacement along the direction of a ray in layer l between the crossingpoints of that ray and two neighboring rays from layer m .The last two tensors, r lm and w lm can be calculated with simple vector arithmetic in a pair-wisemanner among the N l layers in the ray grid. The former is symmetric and both have undefineddiagonals. These do require O( N l ) operations where N l is the number of layers and typically N l =
5. Given these two tensors, arbitrary crossing points of rays from two different layers can bewritten as, r lmij = r lm + j w lm + i w ml . (A.1)By exploiting the constant ray direction and pitch, this tensor replaces numerous calls to sin () , cos () and sqrt () functions with multiplication, addition and array indexing.The location of a crossing point r lmij along the pitch direction of a third layer n may be writtenas, p lmnij = ( r lmij − c n ) · ˆ p n . (A.2)Expanding this in terms of r lmij shows the number of unique vector operations needed to form thistensor is combinitoric in the number of layers (eg, N =
5) and independent from the number ofwires: P lmnij = r lm · ˆ p n + j w lm · ˆ p n + i w ml · ˆ p n − c n · ˆ p n . (A.3)Finally, the typical use of this pitch location is to identify the nearest ray in plane n by its index.This index can be found simply as, I lmnij = f loor ( P lmnij / p n ) . (A.4)– 15 – eferences [1] R. Acciarri et al. Design and Construction of the MicroBooNE Detector. JINST , 12(02):P02017,2017, 1612.05824.[2] B. Abi et al. The Single-Phase ProtoDUNE Technical Design Report. 2017, 1706.07081.[3] M. Antonello et al. A Proposal for a Three Detector Short-Baseline Neutrino Oscillation Program inthe Fermilab Booster Neutrino Beam. arXiv:1503.01520 , 2015, 1503.01520.[4] Babak Abi et al. Deep Underground Neutrino Experiment (DUNE), Far Detector Technical DesignReport, Volume II DUNE Physics. 2 2020, 2002.03005.[5] M. V. Diwan, V. Galymov, X. Qian, and A. Rubbia. Long-Baseline Neutrino Experiments.
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