Multi-Input Interaction Positioning and Signal Demultiplexing With Deep Learning in Semi-Monolithic Detectors

Abstract

Deep learning is increasingly transforming medical imaging by enabling more accurate data interpretation and reconstruction from complex detector signals. In positron emission tomography (PET), accurate localization of photon interactions within detectors is crucial for improving image resolution and diagnostic value. This work focuses on semi-monolithic scintillation detectors, which balance pixelated and monolithic designs, and applies deep learning methods that exploit scintillation light patterns across photosensors to improve interaction positioning. We evaluated how different neural network architectures and combinations of input signals affect positioning accuracy using experimental data from two types of detector arrays: 1) a 1×8 module used in the IMAS total-body scanner and 2) a 1×16 module from a brain-dedicated PET, both coupled to 64-channel photosensor matrices. We compared multilayer perceptron and convolutional neural network, using either reduced 16-channel inputs (obtained via row and column summation) or the full 64-channel configuration, along with energy, time, and engineered features. Results show that deeper architectures and richer inputs improve positioning performance—especially in the depth-of-interaction direction, with gains of around 20%—by better exploiting light-sharing effects between slabs. Finally, we introduced a deep-learning-based signal demultiplexing approach which accurately reconstructs full 64-channel signals from reduced 16-channel measurements with structural similarity index measure above 0.98. This enables the combination of simplified hardware design crucial for data throughput together with the benefits of higher resolution positioning when using 64 signals. This work shows how deep learning, when combined with multiple signal inputs and the learned recovery of full signals from multiplexed data, can enhance the performance of PET instrumentation.

I. Introduction

Positron emission tomography (PET) is a medical imaging technique that provides 3-D images of functional processes in the body by detecting pairs of 511 keV annihilation photons emitted from positron-electron annihilation events [1]. The quality of PET images critically depends on precisely localizing annihilation photon interactions in the detectors of the scanner and measuring their arrival times, both of which are directly influenced by the detector design [2]. PET scanners commonly employ pixelated detectors to achieve excellent timing performance, enabled by light signal confinement that yields a high photon density—crucial for time-of-flight (TOF) information, which enhances image contrast and reduces noise [3], [4]. Additionally, pixelation improves spatial resolution by enabling high positioning accuracy [5], [6], [7], [8]. Alternatively, monolithic detectors can offer higher sensitivity and exploit the spatial (and sometimes temporal) distribution of scintillation light on a photosensor array to determine the 3-D interaction position [9], [10], [11].

Another configuration, semi-monolithic scintillator arrays, combines features of both pixelated and monolithic detectors with pixelation along one direction and a monolithic structure along the other, thus consisting of 1 × N scintillator slabs. This enables simultaneous capabilities of TOF and depth-of-interaction (DOI) measurements, as the light is sufficiently confined within the slabs and its spatial distribution is depthdependent [12], [13], [14], [15], [16], [17]. Providing DOI information is important because it helps mitigate parallax errors caused by distortions arising when interactions occur at different depths in thick detectors, thus improving spatial resolution uniformity across the imaging field of view [18]. Detectors with a semi-monolithic geometry were chosen for the new IMAS long axial field of view PET scanner [19] and the Ultra-High performance Brain (UHB) scanner, a dedicated brain PET system currently under development [20].

Analytical/statistical interaction positioning methods in scintillators have demonstrated high precision [9], [21], [22]. More recently, neural networks have gained prominence, providing excellent timing resolution in pixelated detectors [23], [24], [25], as well as both timing and positioning resolutions in monolithic detectors [10], [11], [26], [27], [28]. For semi-monolithic scintillators, previous studies have successfully shown the usage of machine/deep-learning methods based on gradient tree boosting [14], [16], [17], [29] and multilayer perceptrons (MLPs) [30], the latter being used in the IMAS PET system. These methods rely on energy information, using either the light distribution across silicon photomultipliers (SiPMs) or engineered features also extracted from the energy patterns. However, previous studies also highlighted some correlation between the DOI and the time information, for instance in phoswich detectors [31], fast TOF detectors where the waves of photons are correlated with the DOI [32], [33] and light sharing arrays [34]. Moreover, even though the slabs are optically separated by reflectors, some light sharing can still occur within scintillator arrays [35], suggesting that more inputs and more complex networks could benefit from this position-dependent signal sharing. Therefore, more complex networks, such as convolutional neural networks (CNNs), combined with the usage of time inputs and engineered features might help to enhance positioning accuracy in semi-monolithic crystals.

Furthermore, multiplexing techniques are often essential for managing large data flows, as they reduce the effective number of channels [36]. However, this also raises the need for a more thorough understanding of how multiplexing may impact positioning accuracy. Techniques were recently proposed to perform data reaugmentation through demultiplexing [37], [38], enabling to maintain hardware channel reduction for better data flow rate while still benefiting from a reconstruction of full signal distribution.

In this work, we reexamine the application of deep learning for event positioning in semi-monolithic scintillators, exploring a range from low-feature, shallow-architecture networks to high-feature, deeper-architecture models. Following previous studies [20], [30], we treat MLPs with energy inputs obtained from row- and column-summed SiPM signals as the conventional baseline. Building on this, we introduce additional input features and investigate alternative network architectures. We use experimental data obtained from arrays of the IMAS scanner (a total-body PET) and the upcoming UHB scanner (a brain-dedicated PET), and aim to compare the usage of a reduced set of signals from a channel reduction readout with the full nonreduced signals. We also add time-based information together with the typically used energy information, and we incorporate engineered features to facilitate the training of the MLPs and the CNNs. We then propose a deep-learning-based demultiplexing technique to reconstruct high-resolution signals from reduced data obtained by summing the signals from the rows and columns of SiPM arrays. This approach aims to enable more accurate event positioning while maintaining the benefits of reduced-channel readouts in real (TOF-)PET systems, and is presented here as a complementary analysis building upon the main comparisons of input types and architectures. Overall, this study can help to identify a range of possible positioning resolution depending on the usage of various networks, energy/time information and recovery of full signals from multiplexed data through deep learning approaches.

II. Materials and Methods

A. Semi-Monolithic Detectors

Measurements with three semi-monolithic arrays were performed: one from the IMAS total-body scanner [19] and the two others being candidates for the UHB scanner currently in development [20]. The IMAS detector consists of an array of eight LYSO:Ce rectangular slabs, each with dimensions of 25.8×3.1×20 mm³. The UHB detector geometry has a design modification to improve the packing fraction in the scanner, i.e., a trapezoidal-shaped array consisting of 16 slabs (1.5 mm thick and 20 mm long) with one slanted face, giving length of 25.4 mm at rear end (coupled to the SiPM) and 22.6 mm at the front end. For the IMAS detector and one of the UHB detector, all faces of the scintillators are polished and ESR films are glued in between the slabs and around the whole array. These configurations are hereafter referred to as IMAS ESR and UHB ESR, respectively. For the second UHB detector, the same surface type was used except for the 1.5 mm×20 mm pixelated faces that were black painted. This configuration is referred to as UHB ESR+B. A schematic of the detectors is shown at the top of Fig. 1.

Fig. 1.

Sketches of the (a) UHB ESR array with pinhole collimation and the (b) UHB ESR+B and IMAS ESR arrays with slit collimation.

The three array types were used with complementary purposes. First, the UHB ESR array was studied in detail with a full 64-channel readout, as initial tests showed higher potential for improvement when using more input types and deeper network architectures with this array. Pinhole collimation measurements [Fig. 1(a)] at multiple DOI and monolithic positions enabled a fine-grained characterization of the array. In a second step, we moved toward more scanner-like detectors and measurements, for which we used the selected arrays of the UHB and IMAS (UHB ESR+B and IMAS ESR) together with the electronic channel reduction readout to pass from 64 to 16 outputs by summing the rows and columns of the photosensor array [39], [40]. Also, a collimation was done with a slit instead of a pinhole [Fig. 1(b)], representative of what is used in a scanner-like configuration. As a final step, since reducing inputs may degrade positioning resolution, we tested demultiplexing to recover 64 channels, using the three arrays to assess either demultiplexing accuracy or the potential to enhance positioning resolution from channel-reduced data.

B. Electronic Readout

The arrays were coupled to an 8×8 SiPM matrix with 3.2 mm SiPM pitch from Hamamatsu Photonics (S13361-3075AE-08), read out using the TOFPET2 ASIC from PETsys electronics [41]. For the UHB ESR the standard 64-channel readout was used, while for the UHB ESR+B and IMAS ESR a channel reduction scheme was applied before feeding the signals to the ASIC. Such channel reduction or multiplexing circuit sums the SiPM output along rows and columns allowing to reduce the number of channels (for a single SiPM array) from 64 to 16 [39], [40]. For each array, we selected the SiPM bias voltage (V_b) and ASIC discriminators providing the best tradeoff in timing and energy resolution, as well as slab resolvability. The first discriminator (vth_t1) measures the first timestamp at low voltage threshold; the second (vth_t2) operates at higher voltage threshold to discard dark counts and validate the first event; the third (vth_e) is used for energy validation. The parameter set {V_b, vth_t1, vth_t2, vth_e} was {55V, 5, 25, 20} for the UHB ESR, {54V, 10, 20, 8} for the UHB ESR+B, and {53V, 10, 20, 10} for the IMAS ESR, with the three discriminators in DAC units. These sets were obtained from a front uniform irradiation of the arrays, with a ²²Na radioactive source opposite to the SiPM readout face.

C. Experimental Measurements

1). Pinhole Scan:

The UHB ESR detector was irradiated with a pinhole collimation (2 mm diameter) with 1 mm steps in both the monolithic and DOI directions [Fig. 1(a)]. For all measurements, event filtering was done similarly to [30], including slab selection (choosing the slab(s) coupled to the second SiPM row to minimize edge effects), photopeak selection (within ±15% of the photopeak center), and position filtering (events falling within the central 90% of the DOI and monolithic projections). At each position, data were acquired for 20 min and only positions with at least 500 events after photopeak selection and filtering were kept for the performance analysis. For this scan, a total of 1.05M valid events were acquired, which were then split into 70%, 10%, and 20% for training, validation, and testing, respectively.

2). Slit Scans:

A source collimation using a slit with 0.5 mm width was done for the UHB ESR+B and IMAS ESR arrays. This calibration method (slit instead of pinhole) is used in the systems because it enables faster acquisition, even with a narrow collimator opening, which in turn reduces the contribution of the collimator to the measured resolution. The collimation was performed in two steps: first along the DOI direction with a 1 mm step size, and then along the monolithic direction with a 0.5 mm step size [Fig. 1(b)]. Event filtering was done as for the pinhole measurement and events for each dataset were split into 70%, 10%, and 20% for training, validation, and testing, respectively. For these scans, 111k and 422k events were recorded for the UHB ESR+B array, and 178k and 475k for the IMAS ESR array, along DOI and monolithic directions, respectively.

D. Exploration of Deep Learning Models

In this work, two deep learning models were implemented for interaction positioning: an MLP and a CNN. An exploration of these models was performed using different combinations of energy inputs, time inputs and features for various network architectures, as illustrated in Fig. 2.

Fig. 2.

(Left) Example of a measured signal and the summation along rows and columns. (Right) Schematic of the input types and the different architectures, only shown as illustrative with the true numbers of nodes, convolutional layers, etc. detailed in the main text. The output can be a single regression value (DOI or monolithic) or a dual output with both predictions (for the 2-D pinhole scan). Features can be added deeper in the hidden layers of the networks.

1). Architecture Complexity and Input Types:

For the UHB ESR array with the pinhole scan, four network architectures were tested, combining either a MLP or a CNN with 16 or 64 signals, referred to as MLP16, CNN16, MLP64, and CNN64, respectively. The inputs for MLP64 and CNN64 were directly the full 64 energy signals, whereas the inputs for MLP16 and CNN16 were obtained by summing the signals in rows and columns in postprocessing to emulate a reduction readout. By default, only the energy values were given as inputs to the networks. Among these, MLP16 corresponds to the conventional baseline method [20], [30], from which we explore potential gains by adding features, modifying inputs, and testing alternative architectures.

Time information can also be added as inputs to the networks, either from eight timestamps of the irradiated crystal slab (or SiPM row), or the full 64 timestamps of the array (only for CNN64). Skew correction was applied on the timestamps to correct the offsets between the SiPM channels. Because of the semi-monolithic geometry, a typical event will have most of its energy concentrated along a SiPM row and the ASIC thus typically provides fewer than 64 timestamps, so the unavailable ones were put to zero as with the energy values.

Signal features can furthermore be added to the network. In this work, six engineered features were designed, and all six were consistently included whenever signal features were incorporated into the network with the UHB ESR measurement. The three first were classical analytical predictions of interaction coordinates (see Fig. 1 for the coordinate directions). The pixelated coordinate was obtained from the center of gravity calculated by weighting the SiPM position hits with their energy values [42], the monolithic coordinate from the center of gravity raised to the power of two [43], and the DOI coordinate from the ratio between the integral and the amplitude of the energy signals [44]. The other three features were the variance of the energy signals of each event, the time difference between the fastest and second fastest hits, and finally the time difference between the fastest and the most energetic SiPM hits [20].

From this point on, the use of energy (E), time (T), and features (F) will be indicated alongside the network architecture and signal configuration. For example, CNN64-energy, features, and time (EFT) refers to a CNN with 64 signals, using energy, time, and features, while MLP16-E corresponds to an MLP with 16 signals, using only energy. A schematic of the different numbers of input signals, using energy, time and features is displayed in Fig. 2.

For the UHB ESR+B and IMAS ESR with the slit scans, the MLP16 and CNN16 architectures were tested using the hardware-reduced signals. The timestamps were extracted from the signals summed across the slabs, without skew correction. For these scans, individual SiPM hits are not accessible, so the two timing-based features described before can not be extracted. Only the remaining four features (three analytical predictions of interaction coordinates and the variance of the energy signals) were used when added to the network.

2). Training Procedure and Evaluation Metrics:

We first describe the training setup used for the pinhole scan measurement. A min–max normalization was applied to the inputs and features, separately for energy, time, and features. For the MLPs, energy and time inputs start with distinct networks that are then merged, the CNN16 appends the time inputs as a third column to the 8×2 energy inputs, and the CNN64 adds another channel for the time inputs (red and blue inputs in Fig. 2). For the MLP-based models, fully connected layers were used with varying numbers of hidden nodes. The MLP16 consisted of two hidden layers with 64 nodes each, while MLP64 used two hidden layers with 128 nodes each. ReLU activations were applied after each hidden layer. The CNN16 utilized two convolutional layers with 32 and 64 filters and filter size of 2×2 and 1×1, respectively, followed by two fully connected layers with 64 nodes each. The CNN64 employed a deeper architecture with three convolutional layers, using 32, 32, and 64 filters, and a filter size of 3×3 for feature extraction. This was also followed by two fully connected layers with 64 nodes each. ReLU activations were applied after each convolutional layer and fully connected layer.

The networks were trained using a batch size of 256, optimized with the mean-squared error (MSE) loss function and Adam optimizer, a learning rate of 5 × 10⁻³ reduced by a factor ten at 10% of the total number of epochs. For the DOI or monolithic prediction, the MLP16 and CNN16 architectures were trained for 25 epochs, while the deeper MLP64 and CNN64 models were trained for 30 epochs to allow better convergence. Another possibility introduced in the present study is using a network training having a dual output (DOI and monolithic) instead of using a single network for each coordinate as it is typically done [30]. During the testing phase, the prediction distribution at each position was fitted using a kernel density estimation and the accuracy was evaluated in terms of full-width at half maximum (FWHM), mean-absolute error (MAE), and bias.

For the slit scan measurements, we trained both the MLP16 and CNN16 models using all combinations of energy, time, and features as inputs. Training parameters were consistent with those of the pinhole collimation, though the learning rate was instead reduced by a factor of ten after 25% of the total number of epochs. For CNN16-EFT with the IMAS ESR array, the reduction was applied earlier like for the pinhole collimation, at 10%, as this setting showed slightly better performance. We then evaluated the FWHM, MAE, and bias for each slit position.

Since we previously observed a larger dependence of signal features and time information contained in the signals along the DOI direction [20], the results presented here will primarily focus on DOI predictions rather than monolithic ones, both for the pinhole and slit scans.

E. Signal Demultiplexing

Since the reduced 16 signals represent projections of the original 64 signals, the mapping between the two could be retrieved with deep learning techniques, allowing to reconstruct the full signals when using multiplexing circuitry. This technique, referred to as demultiplexing, was also used for pixelated detectors in [37]. In our case, the demultiplexing was performed using the summed row and column signals as inputs, with the original 64-channel signals as ground truth. We used the uniform front irradiation measurements of the UHB ESR and UHB ESR+B arrays (acquired without channel reduction, see Section II-B). Channel reduction was applied in postprocessing, and neural networks were trained to map from the 16-channel to the 64-channel signals. For each array, models were trained either on the full dataset or on a subset using slabs coupled to the second SiPM row, to minimize edge effects as done in the positioning networks (Section II-D). The full datasets included 155k events for UHB ESR and 105k for UHB ESR+B, while the reduced (second SiPM row) datasets contained 16k and 11k events, respectively. All datasets were split into 70% training, 10% validation, and 20% testing. Training used MSE loss with the Adam optimizer. The learning rate started at 1 × 10⁻³ and was reduced by a factor of 10 at 30% and 60% of the total epochs. Networks were trained for 500 epochs on the full datasets and 100 epochs on the reduced ones.

We used a fully connected residual network that first projects the 16-channel input to 256 units, followed by two residual blocks. Each block consists of two linear layers with ReLU activations and skip connections. The output is then projected down to 64 dimensions through two linear layers interleaved with ReLU activations. To assess reconstruction quality, we tracked image similarity metrics, specifically cosine similarity and structural similarity index measure (SSIM), comparing the reconstructed 64-channel data to the ground truth. The trained networks were then applied to positioning data (from pinhole and slit measurements) to reaugment signals, either from software-reduced inputs (pinhole) or real hardware-reduced data (slit). In the pinhole case, the original 64-channel data is available, allowing direct comparison among MLP16-E, CNN64-E, and CNN64-E with demultiplexed inputs. In the slit case, where 64-channel ground truth is unavailable, we compared MLP16-E to CNN64-E with demultiplexed inputs. In all scenarios, the demultiplexing network was applied to data unseen during its training. This approach therefore evaluates both the fidelity of 64-channel signal reconstruction and its impact on positioning accuracy.

III. Results

A. Energy-Based Inputs and Time-Based Inputs

The energy distribution of the signals among the SiPMs is known to drive most of the interaction position dependence in semi-monolithic detectors, yet the time distribution also contains some dependence, as exemplified in Fig. 3. The heatmaps of the FWHM and MAE performance, obtained with a MLP16 using either only the energy information or only the time information, show a comparison between the input types for the UHB ESR array with the 2-D pinhole scan. Above each heatmap, the average and standard deviation of the resolution values across all positions are reported, as consistently done for all heatmaps presented in this work. The networks here were trained for one ground truth direction at a time even though we had access to two with the pinhole collimation, as it was done in previous works [20], [30]. Line profiles extracted at the example positions also display the FWHM and MAE accuracy comparison while using only energy or only time. The energy inputs provide better FWHM and MAE for all DOI and monolithic positions, but the time inputs are also able to retrieve information about the interaction positions. This motivates to try combining both information types as inputs for the networks for the positioning predictions.

Fig. 3.

FWHM and MAE performance for DOI and monolithic predictions as a function of all positions using only the energy inputs or only the time inputs (UHB ESR with MLP16-E or MLP16-T). Line profiles extracted at the framed regions along an example monolithic or DOI position are shown on the bottom.

B. Architecture Complexity and Input Types

Heatmaps of the FWHM of the DOI prediction performance (UHB ESR) for the different architectures (MLP16, CNN16, MLP64, and CNN64) and types of inputs are shown in Fig. 4. Generally, the usage of 64 signals provides accuracy gain compared to 16 signals, and the CNN also performs better than the MLP. For a simpler model like MLP16, adding the features and the time inputs helps improving more the performance (leftmost column) compared to adding features and time for a more complex like the CNN64 (rightmost column). The MLP16-E model shows a FWHM average of 4.1±1.3 mm, compared to 3.5±1.2 mm for the more complex model CNN64-EFT. The training done for the monolithic direction (plots not shown) gave more marginal improvement (3.0±1.2 mm for MLP16-E versus 2.8±1.0 mm for CNN64-EFT), as expected from the larger importance of time-based inputs and/or features for the DOI positioning [20].

Fig. 4.

DOI prediction performance in FWHM as a function of all the positions for the four architectures (columns) and the four input types (rows) for the UHB ESR array. The average FWHM and associated standard deviation is indicated above each heatmap.

Network trainings were also performed using a dual-output (DOI and monolithic) model (see again Fig. 2) using the data acquired with the pinhole collimation for the UHB ESR array. Compared to previous works, this method therefore uses a single network and optimize both positions simultaneously. Tests revealed the same prediction performance as the trainings using two dedicated networks, yet with a halving of the training time. The heatmaps were similar to Fig. 4 and are therefore not shown.

The accuracy improvement provided by models more complex than the standard MLP16 can be nonstationary as a function of the position. To provide a visual representation of the difference in the predicted values by a simpler model (MLP16-E) compared to a complex model (CNN64-EFT), distributions of predictions are shown in Fig. 5 for nine example positions for a training done on the DOI. The CNN64-EFT distributions have lower bias, and better MAE and FWHM as indicated below each subplot.

Fig. 5.

Examples of DOI predictions of the MLP16-E compared to the CNN64-EFT for nine positions among the monolithic and DOI, obtained for a training on the DOI with the UHB ESR array. The squares added on the heatmap correspond to the physical positions of the subplots on the right side. Comparisons in FWHM, MAE and bias are indicated below each plot.

C. Bias Reduction

We assessed the bias for each position (with training along the DOI for the UHB ESR), and evaluated the standard deviation of the bias values as a metric to assess whether using time-based inputs, features or deeper networks would help flattening the bias (lowering the standard deviation) compared to the standard MLP16-E. The standard deviation of the bias is indeed reduced (Fig. 6), translating into a more uniform positioning accuracy across all the positions. The trends of Fig. 6 show a general reduction of the standard deviation of the bias for more complex architectures and quantity of inputs. An inset plot also displays the percent reduction of the standard deviation of the bias compared to MLP16-E, showing close to 20% improvement for 64-input models with time inputs and/or features. There is also a largest dispersion for MLP16 between input types compared to the other models, indicating that adding features and time provides larger improvement compared to the standard energy inputs. Even though the MLP64 and CNN64 architectures gave strong bias reduction, adding more inputs than the energy provides limited improvement.

Fig. 6.

Standard deviation of the bias of the DOI prediction for the network architectures, when using only energy (E), EFs, ET, and EFT with the UHB ESR array. The inset plot shows the difference and percent reduction of the standard deviation of the bias compared to MLP16-E.

D. Channel Reduction Readout

The FWHM, MAE and bias as a function of the DOI for the measurements with the UHB ESR+B and IMAS ESR arrays are shown in Fig. 7. These results were obtained using both a slit collimation and the channel reduction readout electronics, therefore with only 16 inputs as no demultiplexing was applied here. The performance in this figure compares the simpler model available MLP16-E to the more complex one available CNN16-EFT to show the full potential of using maximum input and network complexity. However, tests with CNN16-E indicated similar performance as CNN16-EFT. Improvements are obtained with the CNN16-EFT compared to a MLP16-E for UHB ESR+B, with a better FWHM (2.5 mm versus 3.0 mm) and MAE (1.3 mm versus 1.5 mm). For the IMAS ESR array, the CNN16-EFT also achieves better FWHM (3.1 mm versus 3.4 mm) and MAE (1.5 mm versus 1.7 mm) compared to MLP16-E. The bias at the edges of the array is also reduced with the CNN. As also observed in Section III-B, adding time inputs and/or features for the monolithic prediction only provided marginal gains (not shown for these measurements), so most of the improvement can be expected more on the DOI prediction when using time and features.

Fig. 7.

Comparison of DOI prediction performance (MLP16-E versus CNN16-EFT) for the slit measurement using the (a) UHB ESR+B array and the (b) IMAS ESR array.

E. Signal Demultiplexing

1). Reconstruction Accuracy of Demultiplexed Signals:

The demultiplexing network accurately reconstructs synthetic 64-channel signals, as illustrated in Fig. 8, which presents visual comparisons between ground truth and predicted signals, as well as similarity metrics. The model achieves consistently high accuracy across datasets, with average cosine similarity values exceeding 0.995 and SSIM values above 0.98. Also, the model seems able to reconstruct signals arising from intercrystal scattering (ICS), such as the one shown in the third example at the top right of Fig. 8, where most of the light is detected in two non-neighboring slabs, ruling out simple light leakage. Both metrics are slightly higher when evaluated on the reduced subset of two slabs coupled to the second SiPM row, compared to the full datasets. This marginal performance drop in the full-slab datasets likely reflects the increased variability in signal distributions on the SiPM array.

Fig. 8.

(Top) Six examples of true and predicted signals after applying the demultiplexing. (Bottom) Cosine similarity and SSIM distributions on the test sets for the different datasets of arrays and selection.

2). Impact on Interaction Positioning Performance:

Using demultiplexed data improves positioning accuracy compared to the reduced 16-channel input, as shown in Fig. 9. For the UHB ESR array with the pinhole scan, the DOI prediction accuracy in terms of FWHM is 4.1±1.3 mm for MLP16-E, 3.5±1.3 mm for CNN64-E with true 64-channel signals, and 3.7±1.4 mm for CNN64-E using demultiplexed signals. In the slit measurements, CNN64-E with demultiplexed input also outperforms MLP16-E across all evaluated metrics (FWHM, MAE, and bias) for both the UHB ESR+B and IMAS ESR arrays. Notably, the demultiplexed IMAS ESR data was reconstructed using a network trained on UHB ESR signals, demonstrating the cross-array generalizability of the demultiplexing approach.

Fig. 9.

DOI prediction performance (a) in FWHM for MLP16-E, CNN64-E and CNN64-E with demultiplexed inputs, using the pinhole measurement on the UHB ESR array, (b) in FWHM, MAE and bias for the MLP16-E and CNN64-E with demultiplexed inputs, using the slit measurement on the UHB ESR+B array, and (c) similarly for the IMAS ESR array.

IV. Discussion

The motivation of using more complex networks and additional inputs arose from the light leakage occurring between slabs of a semi-monolithic crystal array (Fig. 2, left). Despite optical isolation of the scintillators with ESR foils, light confinement within the interaction slab appears to be imperfect. This is likely due to leakage through the crystal-SiPMs coupling layer, but also to ESR reflectivity quenching caused by coupling materials in contact with the reflector [35]. This latter effect can then result in scintillation light transmitting through the reflector, which can then be exploited by a neural network to refine the positioning predictions. ICS events also likely contribute to this light distribution across slabs.

It was shown that the energy information drives most of the positioning capabilities, yet the time information is also correlated with position, albeit with less impact (Fig. 3). The combination of energy with time inputs and engineered features into the networks helped improving the FWHM resolution (Figs. 4 and 5), as well as to reduce the bias (Fig. 6) that is inherent to semi-monolithic detectors [30], [45]. Most of the results presented in this work focused on DOI positioning, as the time inputs and features appeared more informative for DOI estimation than for monolithic positioning [20]. Nonetheless, we still observed some improvements in monolithic positioning, and ongoing developments in radiation instrumentation may eventually yield more multifactorial information to improve resolution in both directions.

Skew-corrected timestamps were used for the pinhole measurements, whereas the raw timestamps were used for the slit measurements with the channel reduction readout. Even without corrections in the latter case, including timing information still improved positioning accuracy, suggesting that the networks can capture the interdependence of normalized timestamp series within events, even in the presence of potential relative offsets. Nevertheless, skew corrections may become necessary when training and testing across different arrays with distinct skew maps.

For both arrays with only ESR, upgrading from MLP16-E to CNN16-EFT resulted in a ~10% gain in FWHM (Figs. 4 and 7). However, IMAS ESR achieved a better absolute FWHM compared to UHB ESR due to the smaller contribution of the collimator (slit with 0.5 mm aperture for the former and pinhole with 2 mm diameter for the latter). For the UHB ESR+B, we performed measurements using both a slit and pinhole collimation, but results were not shown for the latter because of limited gains when using more complex architectures or additional inputs, staying within the same range as the 2 mm collimator diameter. Given that the black painting improves the intrinsic spatial resolution of the array [20], the pinhole collimator contribution was probably more significant in the achievable resolution with ESR+B compared to ESR, limiting the effects of the network tunings. However, when using the 0.5 mm slit collimation, we obtained for UHB ESR+B a FWHM improvement of 17% with CNN16-EFT compared to MLP16-E (Fig. 7).

As raised by this type of study, the performance can be pushed with more information—and one goal was to see some best-performing models—but the classical tradeoff remains as these models need more data per interaction event. The positioning accuracy gain can therefore be weighted depending on the desired performance/complexity compromise. Our results demonstrate the advantage of using all 64 input signals. However, accuracy improvements can also be achieved with more complex network architectures and the incorporation of time/features when using an electronic channel reduction readout (Fig. 7). This reduction readout is currently used in the IMAS scanner and will also be implemented in the UHB scanner.

More specifically, when comparing MLP and CNN architectures, the inclusion of additional inputs plays a key role in achieving similar performance, as seen in Fig. 4. For the 16-channel case, both MLP16 and CNN16 benefit from the addition of features and timing information. In contrast, for the 64-channel case the improvements are smaller for MLP64 and essentially absent for CNN64. MLP64 with features and/or time achieves comparable performance to CNN64 with only energy inputs. Overall, adding inputs improves accuracy relative to the baseline MLP16, and the optimal choice depends on the detector and readout: MLP16 with features and timing is attractive with channel-reduction readout, while CNN64 with energy-only inputs is advantageous when full signal information is available. Since CNN64 outperforms MLP16 because of the additional inputs, demultiplexing offers a path to combine reduced readout with CNN-based estimation.

Notably, we have shown that deep-learning-based demultiplexing effectively alleviate the performance loss associated with using the reduced 16 signals. By accurately reconstructing synthetic 64-channel signals from 16-channel inputs (Fig. 8), this approach enables to maintain the reduction readout hardware necessary for managing high data throughput, while allowing offline signal reaugmentation prior to improve interaction positioning (Fig. 9). We validated the method across three different array types, showing that semi-monolithic arrays with varying geometries can still benefit from a demultiplexing network trained on a single array. In particular, the IMAS ESR array, which contains eight slabs, achieved improved prediction accuracy using a demultiplexing model trained on data from the UHB ESR array that has 16 slabs. In the next steps, we will need to move the process toward implementation at the scanner level. The network must first be trained on calibration data acquired without readout reduction, providing paired 64-channel and 16-channel signals, which can be collected under controlled acquisition conditions as in the present study. Given the expected variability in detector performance across a scanner, it will also be important to determine how much calibration data is necessary to ensure robust generalization of the demultiplexing network in routine use. Recovering ICS events could also be performed to reach optimal positioning performance in semi-monolithic arrays, using various types of inputs and network architectures, together with demultiplexing methods.

In this work, we focused on a relative intracomparison of the arrays depending on input types and architecture complexity. While this was the main objective, it is important to note that the intrinsic performance of semi-monolithic detectors can also be influenced by factors, such as crystal dimensions and surface conditions, SiPMs, and other hardware components [12], [14], [20], [30]. For instance, we observed that slab thickness and surface conditions can affect positioning resolution, as shown in Fig. 7 when comparing the UHB ESR+B and IMAS ESR arrays, with the thinner slabs combined with some black painting generally helping to improve the resolution. Also, some variation in DOI resolution by position was observed (e.g., Fig. 4). Patterns arise from reflections and light propagation effects for events near the center of the slabs, leading to poorer DOI resolution at central positions. As shown in [20], these effects are detector-dependent and can be reduced by using alternative surface treatments (e.g., retroreflector or black paint).

Finally, with the impressive timing performance improvements over the past years, we expect the timing information to become more and more relevant, since the interaction position—even in pixelated crystals (for the DOI)—could be retrieved from timestamp distribution if the timing performance is sufficient [32], [33]. Another aspect worth exploring would be interaction positioning in semi-monolithic scintillators that also produce a fraction of prompt photons [46], [47]. The techniques explored in the present work of adding features and time-based inputs could help to determine more precisely the impact position in scintillation detectors, exploiting the time distribution of prompt photons relative to conventional scintillation photons [48].

V. Conclusion

This work demonstrated that interaction positioning accuracy in semi-monolithic detector arrays can be improved by optimizing deep learning models and extending the number and types of input signals and features. Experiments using semi-monolithic crystal arrays from the IMAS total-body scanner and from the UHB brain-dedicated scanner in development were performed to assess the potential improvements. We compared MLPs and CNNs with different input configurations, ranging from reduced 16-signal row and column summations to the full 64-signal 8×8 SiPM array readout. Incorporating energy, time inputs, and features, we showed that multi-input models and deeper architectures better exploit light-sharing effects between slabs, achieving lower bias, FWHM, and MAE, especially along the DOI direction. Importantly, we also found that MLPs with additional inputs can reach performance comparable to CNNs, while CNNs show their strength when full signal information is available, indicating tradeoffs between model complexity and readout configuration. We finally demonstrated the high accuracy of a deep-learning-based demultiplexing technique in reconstructing 64 outputs from 16 inputs, which translated into better interaction positioning performance. These results show the potential of deep learning models to further refine interaction positioning in semi-monolithic detectors for TOF PET by integrating multiple input types.