Photoelectric detection array channel multiplexing method based on neural network

Abstract

The invention discloses a photoelectric detection array channel multiplexing method based on a neural network, and relates to the field of photoelectric detection. According to the invention, by using the channel multiplexing technology and the convolutional neural network technology, the reading difficulty of a large photoelectric detection array is reduced. A convolutional neural network is combined with a photoelectric array coding and decoding method, decoding of position information after coding and position reconstruction of a coding hit mode are carried out, and the cost of construction, operation and data acquisition is reduced. According to the method, a neural network in the field of computer vision is combined with a particle physical experiment, so that a high-precision decoding process and physical event information restoration in a coding state are ensured.

Description

A method for channel multiplexing of photoelectric detector arrays based on neural networks Technical Field

[0001] This invention relates to the field of photoelectric detection, and in particular to a method for channel multiplexing of a photoelectric detection array based on a neural network. Background Technology

[0002] Photoelectric detection arrays are widely used in industrial detection, radiation medical equipment, and large scientific facilities. With technological advancements and improved photoelectric imaging accuracy, the detection granularity of related equipment is continuously decreasing, while the overall number of readout channels is increasing exponentially. Taking the PandaX experiment as an example, the current PandaX detector uses a photomultiplier tube array for signal collection. The top array consists of 169 3-inch R11410 photomultiplier tubes, and the bottom array consists of 199 3-inch R11410 photomultiplier tubes. For the next-generation PandaX experiment, the detector size will be an order of magnitude larger than the current one, and it will employ new 1-inch readout granularity R12699 photomultiplier tubes. This presents significant challenges to the design and implementation of the entire detector. The surge in the number of readout channels will severely test the photoelectric readout system of the new generation detector, including the design and integration of the entire detector, cooling power, and the achievement of extreme conditions such as low background radiation.

[0003] Therefore, those skilled in the art are dedicated to developing a neural network-based method for channel multiplexing of photodetector arrays. By using channel multiplexing and convolutional neural network techniques, the readout difficulties of large photodetector arrays can be reduced. An effective method combining convolutional neural networks with photodetector array encoding and decoding is proposed. Through decoding the encoded position information and reconstructing the position of the encoded hit pattern, this method can be applied to next-generation detectors. Summary of the Invention

[0004] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is to reduce the difficulty of readout of large photoelectric detection arrays.

[0005] To achieve the above objectives, the present invention provides a method for channel multiplexing of a photoelectric detection array based on a neural network, comprising the following steps: Step 1, channel multiplexing technology encodes multiple channels into a set and reads out the average value; Step 2, a convolutional neural network decodes the original array signal from the multiplexed data.

[0006] Furthermore, in step 1, multiple channels are encoded into a group for unified reading using an encoding method, and the reading within a single group is the average value of the readings of all channels within the group.

[0007] Furthermore, this includes an encoding system for two-dimensional arrays.

[0008] Furthermore, the encoding system clusters the channels and reads them out uniformly.

[0009] Furthermore, the encoding system is obtained using a heuristic algorithm.

[0010] Furthermore, in step 2, ResUnet++ is used for decoding.

[0011] Furthermore, in step 2, the UNet encoder-decoder structure captures spatial information and decodes the signal.

[0012] Furthermore, in step 2, the residual connections of ResNet optimize deep feature learning.

[0013] Furthermore, in step 2, the convolutional neural network learns the spatial correlation of the photoelectron hit density distribution through training samples.

[0014] Further, in step 2, the multiplexed readout signal is decoded and the position is reconstructed.

[0015] This invention reduces the readout difficulties of large photodetector arrays by using channel multiplexing and convolutional neural network techniques. It proposes an effective method combining convolutional neural networks with photodetector array encoding and decoding. Through decoding the encoded position information and reconstructing the position of the encoded hit pattern, the feasibility of channel multiplexing technology in next-generation detectors is demonstrated.

[0016] Channel multiplexing technology works by encoding multiple channels into a single readout using a fixed encoding method. The readout within a single group is the average of the readouts from all channels in that group. Therefore, readouts from large-scale detectors can be multiplexed, reducing the number of readouts required on the multiplexed array by an order of magnitude compared to the number of channels, thus addressing the problem of a significant increase in the number of channels.

[0017] The main convolutional neural networks used in this invention include two types: Residual Connection Network (ResNet) and U-Net (ResUnet++) which combines residual connection modules. ResNet is a deep neural network designed to improve the efficiency of computer vision tasks. This network proposes a residual learning framework, and compared to previous networks, these residual networks have more stable and efficient features for learning samples. U-Net consists of two main components: an encoder and a decoder. The encoder, composed of repeated convolutional modules, follows the traditional convolutional neural network architecture and is responsible for feature extraction and information capture. Each step of the decoder involves upsampling the feature map, then halving the channels of the feature map and connecting it to the corresponding feature map retained by the encoder. By combining the ideas of residual networks with the traditional UNet, the ResUNet series was developed. This invention uses ResUnet++, proposed for medical segmentation scenarios.

[0018] This invention proposes a channel multiplexing technique and designs a closed-loop machine learning-based analysis process, consisting of the following parts. First, a simulation program is developed to generate a training dataset. A physical simulation program based on a next-generation detector is developed to generate the dataset samples required for training, and a usable encoding method is designed. Then, a convolutional neural network is used to decode and multiplex the readout signal and reconstruct the position. Finally, the universality of the method is verified by applying it to LXe detector data. Taking the PandaX-xT and PandaX-4T detectors as examples, the position reconstruction accuracy remains unchanged after channel multiplexing.

[0019] This invention can be applied to next-generation liquid xenon detectors with large photoelectric arrays, large gamma detection arrays, high-precision neutron imaging detectors, and large-area high-granularity photon detectors, reducing the number of channel readouts and alleviating construction, operation, and data acquisition costs. The innovation of this invention lies in its first-ever proposal of a channel multiplexing technology that includes encoding and decoding processes, with application verification using liquid xenon detectors as an example. Furthermore, it combines neural networks from the field of computer vision with particle physics experiments to ensure a high-precision decoding process and the reconstruction of physical event information in the encoded state.

[0020] The surge in the number of detection channels in existing detectors and photoelectric imaging devices has led to severe challenges for readout systems, including high integration difficulty, high power consumption, and cooling issues. This invention utilizes multiplexing technology to encode multiple channels into a single readout average, and then employs a CNN to decode the original array signal from the multiplexed data, thereby significantly reducing the number of readout channels. Channel multiplexing is an effective method for reducing the number of readouts. By encoding multiple photoelectric channels into a group, the output of each group is uniformly the average of all channel readouts, directly reducing the number of readouts and alleviating integration and power consumption pressures. The algorithm reduces information loss during encoding, and then a convolutional neural network accurately decodes the encoded signal. This invention can effectively decode encoded hit patterns across the entire energy range (S2 received photon count from 100keV to 100,000keV), and channel multiplexing does not affect the position reconstruction accuracy.

[0021] While existing channel multiplexing techniques can reduce the number of readout channels, they lose details of the original signal, leading to a loss of accuracy in recovering the positional information contained in the signal. This invention applies convolutional neural network (CNN) technology from the field of computer vision to the signal processing of high-energy physics detectors to achieve efficient and high-precision decoding of the original signal. CNNs, as a mature two-dimensional image denoising and reconstruction technique, utilize the encoder-decoder structure of UNet to capture spatial information and decode the signal, while the residual connections of ResNet optimize deep feature learning. Through training samples (original-encoded hit pattern pairs and position labels), the network learns the spatial correlation of photon distribution. This invention uses a U-shaped network to decode the encoded hit patterns, restoring a clean original signal. ResNet is used to understand the patterns of the encoded distribution, thereby enabling high-precision position reconstruction.

[0022] Compared with existing technologies, this invention has the following obvious substantive features and significant advantages: The photoelectric detector array channel multiplexing technology of this invention is crucial in photoelectric imaging and photoelectric detection systems. By allowing multiple signals to share the same physical channel, it significantly improves resource utilization efficiency, reduces costs, and supports modern multi-service requirements. The advantages are mainly reflected in the following aspects: First, it improves channel utilization and transmission efficiency. For example, in photoelectric detection, the data demand of a single physical event is usually far lower than the maximum capacity of the readout channel. Multiplexing technology can reduce the complexity of the entire system without changing performance, integrate idle bandwidth, and make the utilization rate close to 100%. Second, it reduces the construction and maintenance costs of photoelectric detector arrays. By sharing physical readout channel facilities, the hardware cost and maintenance expenses of photoelectric detectors can be reduced. Third, it enhances system flexibility and reliability. For example, in large scientific installations like PandaX, it can reduce the need for cooling power, the instability of multi-channel connections, and the use of radioactive cables and components, thereby improving the overall performance of the device.

[0023] This invention can be applied to: photoelectric detection channel multiplexing and decoding recovery in equipment such as neutron imaging detectors, gamma cameras, and nuclear medicine imaging; it can provide solutions for future large-scale scientific facilities, such as deep earth experiments (e.g., PandaX), collider experiments (e.g., CEPC), and deep space exploration experiments (e.g., MeGaT), reducing system complexity and thus improving stability; it can also be applied to large-scale imaging equipment such as industrial CT, security inspection, and source term surveys, thereby reducing equipment costs.

[0024] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0025] Figure 1 is a channel multiplexing decoding process and position reconstruction verification diagram of a preferred embodiment of the present invention; Figure 2 is a convergence proof diagram of hit mode decoding of a preferred embodiment of the present invention; Figure 3 is a curve of the decoding hit mode restoration similarity relative to the photoelectrons received at the top of S2 in a preferred embodiment of the present invention; Figure 4 is a comparison diagram of position reconstruction accuracy before and after encoding in a preferred embodiment of the present invention; Figure 5 is a residual difference diagram of Panda-4T verification before and after encoding in a preferred embodiment of the present invention. Detailed Implementation

[0026] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0027] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0028] This invention takes channel multiplexing and decoding in a deep-earth liquid xenon experiment detector as an example. Deep-earth experiments employ dual-phase xenon time projection chamber (TPC) technology, simultaneously recording instantaneous scintillation (S1) and delayed electroluminescence (S2) signals through photomultiplier tube (PMT) arrays at the top and bottom of the detector. This enables complete 3D reconstruction of the event's location and precise energy measurement. The S1 signal originates from the apex of the physical event, producing a relatively uniform light distribution across the upper and lower PMT arrays. For the S2 signal, ionized electrons drift upwards to the liquid xenon surface, where they are extracted into the gaseous xenon (GXe) state and amplified. The combination of S1 and S2 signals reconstructs the event's energy and 3D location. The primary factor used for physical event location reconstruction is the hit pattern left by the S2 signal after being struck by the top detector; this hit pattern effectively maps the event's occurrence. The next-generation PandaX experiment, currently under construction and operating at tens of tons in scale, utilizes 2304 photodetector channels for reconstructing the event's location and energy deposition. This invention uses this application as an example to illustrate the key technologies of photoelectric detection channel multiplexing and decoding. In addition, it has been experimentally verified through the currently running PandaX multi-ton-scale experiment.

[0029] The implementation process of this invention includes three steps: Encoding step. The 2304 readout channels of the PandaX-20T detector are modeled as graph nodes. An edge set is constructed based on the minimum spatial distance constraint d (channels with a spacing less than d are connected), transforming the problem into independent set optimization in graph theory. A genetic algorithm is used to iteratively search for an approximate optimal solution, aiming to minimize the number of unconnected channels within a group (i.e., minimizing the total number of edges in the subgraph). Each group of 12 channels is forced to be non-adjacent and have a spacing satisfying d. Finally, the channels are clustered into 192 groups (each group reads out uniformly), ensuring that the hit pattern after reuse retains the single-cluster photon gradient distribution characteristics, and the position label remains unchanged.

[0030] Decoding process: Using the ResUnet++ deep learning architecture, the encoded hit pattern image is used as input and the original unencoded hit pattern is used as the label; the Adamw optimizer is used to train the model with MSELoss as the loss function, and the model achieves high-precision signal reconstruction and end-to-end recovery of the original photon spatial distribution.

[0031] Location reconstruction process: Using the ResNet18 network, with the encoded hit pattern image as input and the simulated event location as the label, the model achieves high-precision location reconstruction and outputs the location where the event occurred end-to-end.

[0032] The specific implementation process is as follows: 1. Dataset generation from PandaX tens-ton-class detector simulation: Based on the design of the PandaX-20T detector, a detector simulation program was designed based on the Geant4 architecture, and simulation data was generated from it. The top photodetector array consists of 2-inch square photomultiplier tubes (PMTs) arranged in 71 mm equidistant squares, totaling 576 PMTs. Each PMT contains four independent channels, including 2304 readout channels. The program records the spatial distribution of the number of photons received by the top array by simulating the physical process. The next-generation detector has a larger photodetector array, which leads to a corresponding increase in the computation time required for physical simulation. Sampling large-scale physical event samples often requires tens of thousands of CPU hours, which poses a significant challenge to data acquisition. To solve this problem, an S2 simulation parameterization method is adopted, which can significantly shorten the simulation time.

[0033] To process simulated data, channel spacing was eliminated to reduce image resolution and sparsity of positional feature information on the plane. The smaller image size also results in lower training resource consumption. Therefore, the image format is... Each luminous pixel represents a channel. At the end of the data processing pipeline, to make the method applicable to more engineering scenarios, the grayscale image is copied to each image channel, making it a three-channel image. The location label is the two-dimensional light source coordinates (x, y) corresponding to each light source simulation event, which is then normalized. To ensure the accuracy of location reconstruction, image data augmentation operations (such as random horizontal / vertical flipping) are not included in the preprocessing flow. Light source simulations with different numbers of photons received by the top S2 have produced diverse hit patterns at the same light source location.

[0034] 2. Channel multiplexing coding process

[0035] This invention develops an encoding system for two-dimensional arrays. This system clusters channels that meet specific conditions and reads them out uniformly, thereby reducing the number of readout channels. The simulations and experiments used only generate single-point events; therefore, the hit patterns exhibit single-cluster clusters of received photons, and these clusters show a clear gradient distribution from the center to the periphery. Convolutional neural networks can recognize this pattern and reconstruct its location. To ensure that the hit patterns retain information after channel multiplexing, this invention proposes a concise scheme to guarantee that the hit patterns retain the characteristics of single-cluster gradients after channel multiplexing. Specific requirements are as follows: encoded channels within the same group must not be adjacent and must maintain a minimum spacing.

[0036] This problem can be transformed into the independent set problem in graph theory. An independent set is a set of non-adjacent vertices in a graph. An independent set S consists of multiple vertices, where no two vertices are connected by an edge. This also means that each edge in the graph has at most one vertex belonging to S. This invention employs a heuristic algorithm to obtain an encoding method that approximately satisfies the requirements of the problem.

[0037] The solution is as follows: 1. Set the minimum spatial distance d between adjacent vertices in the coding group, set the number of vertices n in each group, traverse the Euclidean distance between each channel in the detector (taking the channel as a node), establish an edge connection between channels with a distance less than d, and construct graph G(V,E). Graph G is obtained by modeling the detector readout system. Node V represents a channel, and the edge E of a node represents that the distance between the nodes is less than d.

[0038] 2. Encode all vertices in the graph into independent sets as much as possible, with n vertices in each set, and search for approximate solutions for the independent sets based on a genetic algorithm.

[0039] Genetic algorithms are optimization techniques inspired by Charles Darwin's theory of natural selection and evolution. They utilize biological processes such as selection, crossover, and mutation to efficiently explore solutions. Genetic algorithms iteratively run on a set of candidate solutions, performing selection, crossover, and mutation operations based on fitness values ​​to gradually evolve a better solution. The simulated detector array contains 2304 channels, grouped into sets of 12, meaning a total of 192 readout channels after encoding. The encoding groups (which can also be described as subsets of vertices in graph G) aim to minimize the total number of edges in these subsets.

[0040] in The partitioning method for graph G, Represents a subset of graph G. and This represents the number of vertices and edges in the subset. The formula means: find a subset that meets the condition that the subset has 12 vertices, and then minimize the total number of edges in the subset.

[0041] The encoding process produces the same amount of encoded image data as the original hit pattern, with the position labels remaining unchanged before and after encoding.

[0042] 3. Channel multiplexing decoding process

[0043] To achieve high-precision decoding of encoded hit patterns, this invention proposes a decoding process using ResUnet++ for channel multiplexing technology, with the network structure shown in Figure 1.

[0044] Model input and output

[0045] From a reproducibility perspective, the effectiveness of decoding encoded hit patterns to unencoded states on a simulated dataset was evaluated. A ResUnet++ model was used, trained with the Adamw optimizer, and a batch size of 128. The weight decay parameter in the optimizer was 3 × 10⁻⁶. -5 Leave the rest of the configuration as default. Set the initial learning rate to 2.5 × 10⁻⁶. -4 Subsequently, the value gradually decreased to 1×10 over 50 training epochs. -4 A cosine decay learning rate scheduling scheme is used. The input image size is... The pixel count and output image size remain unchanged. The dataset consists of data pairs with encoded hit patterns as features and original hit patterns as labels. The model weights are initialized using the He scheme. Given the dataset size of 1e6 and the significant differences between the patterns and traditional image data, no pre-trained parameters are used in any network. The loss function is MSELoss. Training and testing were both performed on an Nvidia A100 GPU. The model training achieved good convergence and avoided overfitting, as shown in Figure 2.

[0046] result

[0047] The Structural Information Similarity (SSIM) algorithm is used to evaluate the similarity between patterned images before and after dimensionality reduction. SSIM decomposes the similarity evaluation process into three comparison dimensions: brightness, contrast, and structure. Assuming x and y are two non-negative image signals that are already aligned, they are defined as follows:

[0048] in It is the mean intensity (discrete signal). Same as above. and That's the standard deviation (the square root of the variance); the rest are constant terms. Defined as:

[0049] To present the results more intuitively, the SSIM values ​​are linearly projected onto the (0,100) interval:

[0050] The quantization results of the hit pattern decoding are shown in Figure 3. After processing with the trained ResUnet++, the output image of the encoded hit patterns in the test dataset showed no significant difference from the unencoded original patterns. Furthermore, the trend in SSIM similarity confirms that the decoding accuracy increases with the number of photon electrons received at the top of S2. Events in the high-energy region exhibit clearer characteristics.

[0051] 4. Reconstruction and verification of the position of the hit pattern in the encoding state

[0052] In addition to decoding, to further verify the preservation of positional information of the encoded patterns and the learning ability of the convolutional neural network to the encoded positional information, positional reconstruction verification of the encoded state hit pattern was added.

[0053] The network structure is shown in Figure 1. Compared to traditional image recognition tasks, considering that the hit patterns simulated by the detector have simpler and clearer features, a ResNet-18 network backbone structure is adopted. The linear layer that outputs multi-class classification is modified to (x,y) coordinates, and its activation function is removed. This network contains a total of 18 layers, including 4 residual blocks (4 layers), initial... Convolutional layers and finally fully connected layers. A ResNet with regression layers will be used for location reconstruction tasks.

[0054] Input and Output

[0055] Hit patterns simulated by the detector are used as input to the model. The network is trained on two separate datasets: one with encoded hit patterns and the other with original hit patterns. The output is the predicted event location based on the hit patterns. The datasets include an encoded hit pattern dataset and an original hit pattern dataset, each containing 210,000 samples (training set) and 90,000 samples (validation set). These datasets consist of hit pattern as feature-location as label data pairs. Evaluation is based on the standard deviation of the horizontal deviation (deltax) between the reconstructed location and the simulated real location.

[0056] result

[0057] As shown in Figure 4, in the high-energy region ( Within this range, there was no significant difference in the accuracy of location reconstruction uncertainty between the encoded and original hit patterns. In this comparison, the original hit pattern performed better in the low-energy region. For signals with small charges, the encoding process further disrupts the spatial distribution of the signal, leading to difficulties in accurate reconstruction. The accuracy of location reconstruction based on convolutional neural networks is positively correlated with the quality of pattern information, which is consistent with the results of pattern decoding experiments.

[0058] 5. Verify the location reconstruction process in the PandaX-4T experiment.

[0059] The channel multiplexing coding and relocation reconstruction process was applied to the Panda-4T experiment currently operating in Jinping, Sichuan, completing the closed-loop verification from simulation to experiment. The PandaX-4T detector is in its mature data acquisition phase. Its top TPC detector layout consists of 169 photomultiplier tubes arranged in a concentric array. Compared to the next-generation detector targeted in this invention, its readout channels are reduced by an order of magnitude, thus reducing the number of individual coding groups to two PMTs per group. Real experimental data, compared to simulated data, has higher noise and lower stability. To make the data values ​​more stable and the mode characteristics clearer, the data was appropriately filtered based on location reconstruction and energy reconstruction: the event location radius satisfies... The event energy is higher than .

[0060] Network Structure

[0061] ResNet-18 is still used as the network for location reconstruction, as shown in Figure 1.

[0062] Input and Output

[0063] Hit patterns obtained from detector simulations are used as model input. The network is trained on two separate datasets: one with encoded hit patterns and the other with original hit patterns. The output is the predicted event location based on the hit pattern. The datasets include an encoded hit pattern dataset and an original hit pattern dataset, each containing 143,600 samples (training set) and 19,900 samples (validation set), consisting of hit pattern as feature-location as label data pairs. The residuals of the R² distribution reconstructed from the 2D location are used as the criterion for evaluating the PandaX-4T experimental data because the point density of randomly uniformly distributed points is uniformly distributed over the area rather than the radius. Histogram counts (bins=500) are performed on the R² obtained before and after encoding, defined as... and Then the residuals (Res) are calculated.

[0064]

[0065] result

[0066] As shown in Figure 5, it can be observed from the two curves representing the r² distribution before and after encoding that the residual remains constant throughout the entire R² range. The experimental results of PandaX-4T validated the channel multiplexing technology in simulating the large detector array of PandaX-20T. Even when the detector is equipped with only 169 photomultiplier tubes, the channel multiplexing technology effectively reduces the number of readouts without significantly affecting position reconstruction.

[0067] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for channel multiplexing of a photoelectric detection array based on a neural network, characterized in that, Includes the following steps: Step 1: Channel multiplexing technology encodes multiple channels into a set and reads out the average value; Step 2: Convolutional neural network decodes the original array signal from the multiplexed data.

2. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 1, characterized in that, In step 1, multiple channels are encoded into a group and read out uniformly using an encoding method. The readout within a single group is the average of the readouts from all channels within the group.

3. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 2, characterized in that, Includes an encoding system for two-dimensional arrays.

4. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 2, characterized in that, The encoding system clusters the channels and reads them out uniformly.

5. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 2, characterized in that, The encoding system is obtained using a heuristic algorithm.

6. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 1, characterized in that, In step 2, ResUnet++ is used for decoding.

7. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 1, characterized in that, In step 2, the UNet encoder-decoder structure captures spatial information and decodes the signal.

8. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 1, characterized in that, In step 2, the residual connections of ResNet optimize deep feature learning.

9. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 1, characterized in that, In step 2, the convolutional neural network learns the spatial correlation of the photoelectron hit density distribution through training samples.

10. The method for channel multiplexing of a photoelectric detection array based on a neural network as described in claim 1, characterized in that, Step 2 involves decoding and multiplexing the readout signal and reconstructing the position.

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