Physics-guided multi-channel attention learning for GPR imaging of hidden anomalies in historic masonry

Ground-penetrating radar (GPR) is a non-destructive electromagnetic method for high-resolution imaging of hidden structures and anomalies. However, its application to historic masonry remains challenging because heterogeneous brick–mortar materials, irregular interfaces, multiple scattering, signal attenuation, and environmental noise can obscure the responses of small or weak internal anomalies. This study proposes a physics-guided deep learning framework for imaging voids, delamination, cracks, and moisture-affected zones in heterogeneous historic masonry. Here, “physics-guided” refers to incorporating physically interpretable GPR attributes into the learning process to provide complementary waveform, reflection-energy, and structural-boundary information. A synthetic GPR dataset was first generated through time-domain electromagnetic forward modeling of brick–mortar structures containing anomalies with variable geometries, dielectric properties, positions, and noise levels. Each B-scan was represented using three complementary channels: the B-scan, the amplitude envelope obtained through the Hilbert transform, and the gradient magnitude. These channels preserve the original waveform characteristics, emphasize reflected energy, and highlight local structural boundaries, respectively. A physics-guided attention U-Net, termed PG-AttUNet, was then developed to integrate these representations. Attention gates were introduced into the skip connections to suppress clutter-dominated features while retaining responses associated with potential internal anomalies. On the synthetic test dataset, the proposed method achieved a mean squared error of 0.0053, a peak signal-to-noise ratio of 22.76 dB, and a structural similarity index of 0.927, outperforming conventional convolutional neural network, U-Net, and multi-input baseline models. Application to field GPR data acquired from a historic masonry structure produced more spatially continuous anomaly maps with fewer scattered false detections. The detected anomalies were spatially consistent with potential crack- or seepage-related pathways inferred from the radar attributes. Because direct field labels were unavailable, the field predictions are interpreted as probabilistic indications rather than deterministic structural reconstructions. These results demonstrate that integrating physically meaningful electromagnetic attributes with attention-based learning can improve the robustness and interpretability of GPR anomaly imaging in heterogeneous cultural-heritage materials.

Historic masonry structures are important components of the built cultural heritage, preserving information on historical construction techniques, materials, and architectural development (ICOMOS, 1964; Feilden, 2003). Their highly heterogeneous composition, together with long-term environmental exposure and material aging, can lead to internal voids, delamination, cracks, weakened mortar joints, and moisture-affected zones (Binda et al., 2000; Roca et al., 2010; Lourenço, 2002). Because these anomalies are often concealed beneath apparently intact surfaces, non-destructive evaluation is essential for heritage diagnosis (McCann and Forde, 2001; Helal et al., 2015). Ground-penetrating radar (GPR) is particularly suitable for this purpose because of its portability, rapid acquisition, high spatial resolution, and sensitivity to contrasts in electromagnetic properties (Maierhofer, 2003; Davis and Annan, 1989). It has therefore been widely used to investigate hidden interfaces, cavities, delamination, moisture variations, and concealed architectural elements (Daniels, 2004; Jol, 2009).

GPR records electromagnetic energy reflected or scattered by contrasts in dielectric properties (Annan, 2009; Lai et al., 2018). Radar-wave responses depend on permittivity, conductivity, antenna frequency, and target geometry, and are therefore sensitive to voids, cracks, and moisture variations (Alani and Tosti, 2018; Laurens et al., 2002). Previous studies have demonstrated the effectiveness of GPR for architectural investigation, masonry diagnosis, and moisture assessment (Pérez-Gracia et al., 2000; Santos-Assunção et al., 2014; Negri and Aiello, 2021; Pérez-Gracia et al., 2024). However, irregular brick and mortar geometry, rubble infill, restoration materials, surface roughness, and local moisture variations generate complex scattering and overlapping reflections (Bavusi et al., 2010; Nuzzo et al., 2010). As a result, weak responses from small voids, cracks, or delamination may be difficult to distinguish from normal masonry interfaces (De Donno et al., 2017). Filtering, denoising, missing-trace reconstruction, and small-target detection can improve data quality (Wang W. et al., 2025; Feng et al., 2024a; Zhou et al., 2025; Chen et al., 2024), but cannot completely eliminate this interpretational ambiguity.

Physics-based imaging and inversion provide more direct links between radar observations and subsurface structure. Forward modeling supports wavefield analysis and synthetic-data generation (Liu S. et al., 2025), while migration-based methods such as reverse time migration (RTM) and least-squares RTM can improve reflector localization and image resolution (Wang et al., 2023; Feng et al., 2023; 2024b). Full-waveform inversion (FWI) further enables quantitative estimation of electromagnetic properties, but is affected by nonlinearity, cycle skipping, initial-model dependence, and high computational cost (Busch et al., 2014). Super-resolution strategies, deep priors, and external geological constraints have been introduced to improve efficiency and stability (Wang X. et al., 2025; Huang et al., 2026; Feng et al., 2024c). Nevertheless, iterative imaging and inversion remain computationally demanding for rapid interpretation of large and heterogeneous GPR datasets.

Deep learning offers an alternative by learning nonlinear mappings from GPR observations to anomaly or dielectric-property representations. Early neural and pattern-recognition methods focused on characteristic radar signatures (Gamba and Lossani, 2000; Dou et al., 2017), while encoder–decoder networks enabled pixel-level inversion and anomaly reconstruction (Tong et al., 2020; Xie et al., 2020). Subsequent studies extended learning-based GPR inversion to tunnel linings, heterogeneous media, and three-dimensional reconstruction (Liu et al., 2021; Dai et al., 2022; 2023). More recent approaches have incorporated model-driven parameters, multi-path feature representations, improved encoder–decoder architectures, adversarial learning, diffusion models, and closed-loop learning (Wang et al., 2022a,b; Xu et al., 2025a,b; Huang et al., 2025a,c,b).

Recent developments also highlight the value of complementary feature modeling and fusion. DFBSNet separates and adaptively fuses low- and high-frequency representations to enhance anomaly-sensitive features in remote-sensing anomaly detection (Yao et al., 2026). In GPR applications, CIGGAN employs feature extraction and fusion to generate diverse radar images from combined void and background information, demonstrating the potential of feature-level fusion for improving GPR data representation and learning (Tian et al., 2025). Related anomaly-detection studies further demonstrate the value of background modeling and complementary feature fusion. S3CRAD combines superpixel-guided background inpainting with multi-feature fusion and spatial–spectral constraints to enhance anomaly–background separation (You et al., 2026), whereas DSFNet employs dual-stream spatial–spectral feature fusion to exploit complementary spectral and spatial information (Wu et al., 2026). These studies provide additional motivation for combining complementary representations when distinguishing weak anomalies from complex backgrounds. Although these methods greatly improve inference efficiency, their performance still depends on training-data representativeness and the consistency between synthetic and field observations.

A further limitation is that GPR B-scans are often treated mainly as ordinary images, while physically meaningful wavefield information is not explicitly emphasized. Recent studies have therefore introduced radar attributes and physical knowledge into learning frameworks. Envelope information has been used to emphasize reflection energy (Huang et al., 2025d), while physics-guided diffusion has incorporated electromagnetic-wave information into probabilistic signal reconstruction (Liu J. et al., 2025). These studies indicate that physics guidance can be introduced not only through explicit forward operators or physics-based losses, but also through physically interpretable input representations, prior information, and feature-selection mechanisms.

Following this idea, the present study introduces physics guidance through the representation and adaptive selection of GPR features rather than through a fully physics-constrained loss function. Each GPR profile is represented by three complementary channels: the B-scan, the amplitude envelope, and the gradient magnitude. These channels preserve waveform information, emphasize reflection energy, and highlight local structural boundaries, respectively. Unlike a standard multi-channel attention U-Net that directly treats multiple inputs as generic image channels, the proposed PG-AttUNet constructs its input channels from physically interpretable GPR attributes with complementary electromagnetic meanings. In addition, the attention gates are used not merely for generic feature enhancement, but to selectively suppress features dominated by background clutter, direct-wave energy, and multiple reflections while retaining anomaly-related responses. Therefore, the proposed framework combines physically meaningful feature construction with attention-guided feature selection, rather than relying on conventional multi-channel image fusion alone.

The main contributions are threefold. First, a synthetic GPR dataset is constructed using heterogeneous brick–mortar models containing voids, delamination, cracks, and moisture-affected zones with variable geometries, electromagnetic properties, positions, and noise levels. Second, a physics-guided multi-channel representation combining the B-scan, amplitude envelope, and gradient magnitude is developed to provide complementary waveform, energy, and boundary information. Third, an attention-gated feature-selection strategy is introduced to suppress clutter-dominated responses while preserving anomaly-related features, thereby improving anomaly localization and reducing false detections. The framework is evaluated using both synthetic and field GPR data from a historic masonry structure. Because independent field ground truth is unavailable, the resulting anomaly maps are interpreted as probabilistic geophysical indications rather than deterministic reconstructions of internal damage.

The proposed framework comprises four main stages: construction of heterogeneous masonry models, time-domain electromagnetic forward simulation, extraction of physically interpretable GPR attributes, and pixel-wise anomaly prediction using the proposed physics-guided attention U-Net (PG-AttUNet). Rather than treating the GPR B-scan solely as a conventional image, the framework combines B-scan waveform information with amplitude-envelope and gradient-magnitude representations. These three channels provide complementary information on waveform polarity, reflected energy, and local structural boundaries.

Representative masonry models containing voids, delamination, cracks, and moisture-affected zones were first constructed. Electromagnetic parameters were then assigned to the brick, mortar, and anomalous regions, and the corresponding radar responses were generated through forward modeling. The B-scan, amplitude envelope, and gradient magnitude were normalized and stacked to form a three-channel input. PG-AttUNet subsequently maps the multi-channel GPR representation to a pixel-wise anomaly-probability map.

In this study, the term “physics-guided” refers specifically to the incorporation of radar attributes derived from electromagnetic responses and to the selective transmission of anomaly-related features. It does not imply that Maxwell’s equations are explicitly embedded as a differential-equation residual in the loss function.

Masonry anomaly conceptualization and sample modeling

Historic masonry is generally composed of spatially variable combinations of brick, stone, mortar joints, rubble infill, and materials introduced during earlier repairs. Such heterogeneity produces complex electromagnetic responses even in the absence of deterioration. To represent the principal internal conditions relevant to the present study, four anomaly types were considered: voids, delamination, cracks, and moisture-affected zones.

Figure 1 illustrates the conceptual forms of these anomalies. Voids were represented as air-filled regions caused by localized material loss. Delamination was modeled as a thin air gap separating adjacent masonry layers. Cracks were represented as narrow and potentially irregular discontinuities cutting through bricks and mortar joints. Moisture-affected zones were represented by regions with elevated relative permittivity caused by increased water content.

The dimensions and electromagnetic properties shown in Figure 1 are representative rather than fixed values. In the synthetic dataset, the position, depth, size, orientation, and morphology of the anomalies were varied to prevent the network from learning only a small number of predefined geometries. Variations in masonry properties and noise conditions were also introduced so that the samples represented a range of possible radar responses rather than a single idealized wall.

The synthetic dataset contained a total of 1,000 samples, comprising four representative anomaly categories: voids, delamination, cracks, and moisture-affected zones. For each anomaly category, 250 independent synthetic samples were generated by varying the anomaly geometry, position, depth, size, orientation, electromagnetic properties, and noise conditions. After sample generation, the complete dataset was randomly shuffled and divided into training, validation, and test sets using a ratio of 7:2:1, corresponding to 700, 200, and 100 samples, respectively. The training set was used for network optimization, the validation set was used to evaluate model performance during model development, and the test set was kept separate for the final quantitative and qualitative evaluation. No sample was shared among the three subsets.

Clay bricks and cement-based mortar were used to construct the basic numerical background. The brick and mortar units were represented separately instead of being replaced by a homogeneous equivalent medium. This design allowed reflections and scattering associated with normal brick–mortar interfaces to coexist with the responses generated by internal anomalies, thereby increasing the similarity between the synthetic B-scans and measurements acquired in heterogeneous masonry.

Dielectric modeling

The radar response of masonry is primarily controlled by the spatial distribution of dielectric permittivity and, to a lesser extent, electrical conductivity and magnetic permeability. The two-dimensional relative-permittivity model is expressed in Equation 1. where ε r (x, z) denotes the relative permittivity at horizontal position x and depth z; N m is the total number of material and anomaly classes included in the model; m = 1,2, …, N m is the material-class index; and ε r, m is the relative permittivity assigned to the m -th class. The spatial indicator function χ m (x, z) is explicitly defined in Equation 2. where Ω m denotes the spatial region occupied by the m -th material or anomaly class. Each spatial location is assigned to one class, such that ∑ m = 1 N m χ m (x, z) = 1 throughout the modeled domain.

The representative relative-permittivity values used for the brick, air-filled anomalies, and moistureaffected regions are given in Equations 3–5. whereas the mortar joints were assigned slightly higher values to preserve the dielectric contrast between the two principal masonry components. The purpose of this assignment was to reproduce the basic electromagnetic heterogeneity of a brick–mortar wall rather than to represent the exact properties of one specific historic structure.

Air-filled voids, delamination gaps, and dry cracks were assigned relative-permittivity values close to

Moisture-affected regions were assigned substantially higher effective permittivities because pore water increases the bulk dielectric constant of masonry. In the representative numerical models, the relative permittivity of these zones was mainly varied within the approximate range

Figure 2 presents four representative permittivity models and their corresponding simulated GPR responses. The examples include an inclined chain of voids, two delamination interfaces, an irregular crack containing a locally enlarged region, and a moisture-affected zone containing a localized air void. These examples show that different anomaly geometries and dielectric contrasts produce distinct combinations of hyperbolic reflections, continuous reflection events, diffraction patterns, and travel-time changes.

GPR data generation and input preprocessing

For each dielectric model, the corresponding GPR B-scan was generated through time-domain electromagnetic forward modeling. The simulated B-scan retained the complete radar response, including direct-wave energy, reflections from normal brick–mortar interfaces, diffraction, multiple scattering, and reflections associated with the modeled anomalies. The B-scan was therefore not constructed by extracting only the anomaly-related reflection region.

No direct-wave removal, background subtraction, time gating, or anomaly-region cropping was applied before the data were used for network training. The complete B-scan was retained as the first input channel. The amplitude envelope was calculated from the complete B-scan to emphasize the spatial distribution of reflected energy, whereas the gradient magnitude was calculated to highlight local waveform variations and structural boundaries. The three representations retained the same spatial and temporal dimensions, were normalized to a common numerical range, and were then stacked to form the three-channel input to PG-AttUNet. Figure 3 illustrates the physics-guided three-channel representation, including the B-scan, amplitude envelope, and gradient magnitude.

Physics-guided attention U-Net

The architecture of PG-AttUNet is shown in Figure 4. The network follows an encoder–decoder structure with skip connections, but attention gates are introduced before encoder features are transferred to the corresponding decoder layers. The network receives the three-channel tensor X and produces a single-channel anomaly-probability map.

Encoder

The encoder consists of convolutional blocks and downsampling operations. Each convolutional block includes convolution, batch normalization, and a rectified linear unit activation. For an input feature map X (l), The output of a convolutional block at level l is expressed in Equation 6. where W (l) and b (l) are learnable convolutional weights and biases, ∗ denotes convolution, BN (⋅) denotes batch normalization, and δ (⋅) denotes the ReLU activation function.

After each downsampling operation, the spatial size of the feature maps decreases while the number of feature channels increases. As shown in Figure 4, the encoder channel dimensions increase progressively from 64 to 128, 256, 512, and 1,024. The shallow layers primarily represent local waveforms and reflection boundaries, whereas the deeper layers encode larger-scale contextual and morphological information.

Attention-gated skip connections

Standard U-Net skip connections directly concatenate shallow encoder features with decoder features. For GPR data, these shallow representations may contain direct waves, strong brick–mortar reflections, multiple scattering, and noise in addition to anomaly-related information. Directly transferring all shallow features may therefore introduce irrelevant responses into the decoder. The attention-gated skip-connection mechanism is formulated in Equations 7–9.

For an encoder feature map x and a gating feature g from the decoder, an intermediate attention representation is calculated as where W x and W g are learnable transformations and b α is a bias term. The spatial attention coefficient is then obtained from where W α is a learnable convolutional transformation and Sigmoid (⋅) maps the coefficient values to the interval [0, 1].

The refined skip feature is where ⊙ denotes element-wise multiplication. Encoder responses assigned low attention coefficients are suppressed, whereas spatial features considered relevant to the decoder context are retained.

Decoder and probability output

The decoder gradually restores the spatial resolution of the feature maps. At each scale, the lower-resolution decoder feature is upsampled and concatenated with the corresponding attention-refined encoder feature. The decoder operation and probability output are described in Equations 10–12. where Up (⋅) denotes upsampling and Concat (⋅) represents channel-wise concatenation. The concatenated feature is processed by convolutional layers:

At the final decoder layer, a 1 × 1 convolution maps the feature representation to a single channel. A sigmoid function then produces the anomaly-probability map: where W o and b o are the weights and bias of the output layer. Each element P i lies between zero and one and represents the predicted probability that the corresponding pixel belongs to an anomalous region.

Label generation and training strategy

The network was trained using paired three-channel radar inputs and binary label maps. Because the locations and geometries of the synthetic anomalies were known during model construction, the corresponding reference mask could be generated directly from the numerical model. Pixels belonging to the void, delamination, crack, or moisture-affected regions were assigned a value of one, whereas background masonry pixels were assigned a value of zero. The reference-label definition and training losses are given in Equations 13–16. where Ω anom denotes the set of pixels occupied by the modeled anomalies.

Because anomaly pixels generally occupy only a small fraction of the complete B-scan, the training task is characterized by class imbalance. A combined Dice and binary cross-entropy loss was therefore adopted: where λ 1 and λ 2 control the relative contributions of the two terms.

The Dice loss was defined as where p i is the predicted probability of pixel i, g i is the corresponding binary label, M is the total number of pixels, and ϵ is a small constant that prevents division by zero. This term directly constrains the overlap between the predicted and reference anomaly regions.

The binary cross-entropy loss was written as whereas the Dice term emphasizes regional overlap and reduces the influence of class imbalance, the binary cross-entropy term constrains the classification of individual pixels. Their combination encourages both spatially coherent anomaly reconstruction and pixel-level discrimination.

The network parameters were optimized using the Adam optimizer. The initial learning rate is defined in Equation 17.

The batch size was 16 and the maximum number of training epochs was 200. Model performance was monitored using a validation dataset. Training was terminated when the validation loss no longer decreased for several consecutive epochs, thereby reducing unnecessary optimization and limiting overfitting. The model associated with the best validation performance was retained for subsequent synthetic and measured-data evaluation.

Experimental design

The proposed framework was evaluated using both synthetic GPR data and field measurements acquired from a historic masonry structure. The synthetic dataset contained representative internal anomalies, including discrete voids, delamination interfaces, irregular cracks, moisture-affected zones, and combinations of different anomaly types. These anomalies were embedded within heterogeneous brick–mortar backgrounds to reproduce the complex reflections and scattering expected in masonry environments.

The field GPR data represented a more complex practical condition, with additional uncertainties associated with antenna coupling, surface conditions, material heterogeneity, multiple scattering, attenuation, and environmental noise. The synthetic data were therefore used for controlled quantitative evaluation, whereas the field data were used to examine the practical behavior of the proposed method under realistic conditions.

All models were trained using the same data partition, reference labels, and optimization strategy to ensure a consistent comparison. Model performance on the synthetic test dataset was evaluated using mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM). Lower MSE indicates smaller pixel-level prediction errors, whereas higher PSNR and SSIM values indicate improved reconstruction quality and structural consistency.

Physics-guided feature representations

Figure 5 presents representative raw GPR profiles and their corresponding amplitude-envelope and gradient-magnitude representations. The B-scans retain the complete recorded wavefield, including direct waves, reflected events, diffractions, multiple scattering, phase variations, and background interference. Although the raw profiles contain the most complete waveform information, weak anomaly-related responses are not always readily distinguishable from the heterogeneous masonry background. The amplitude-envelope images provide a more concentrated representation of reflected energy. Hyperbolic and localized responses become more visually continuous because the envelope suppresses rapid positive–negative waveform oscillations. This representation is particularly useful for identifying regions in which strong energy is distributed over a spatially coherent area. However, high envelope amplitudes are not uniquely associated with anomalies, because strong normal interfaces and direct-wave energy may produce similar responses. The gradient-magnitude images emphasize rapid variations in both the lateral and temporal directions. Reflection boundaries, discontinuous phase axes, diffraction flanks, and locally sharp waveform variations are consequently enhanced. This representation provides complementary information on anomaly morphology and boundary position. Nevertheless, gradient operations can also increase the visibility of high-frequency noise and small-scale background variations. The three representations therefore contain different but complementary information. The B-scan preserves waveform and phase characteristics, the envelope describes reflection-energy distribution, and the gradient magnitude emphasizes local boundaries and discontinuities. Their joint use avoids relying on any single attribute for anomaly identification.

Synthetic data results

Qualitative comparison

Figure 6 compares the predicted anomaly maps for five representative synthetic cases. The reference masks include discrete voids, layered delamination, a vertically extended irregular crack, a spatially distributed moisture-affected region, and a composite case containing more than one anomaly type. The CNN model identifies some high-contrast anomaly regions but generates numerous scattered responses. Its predicted anomalies are spatially fragmented, and several background reflections are incorrectly interpreted as anomalous regions. The limited multi-scale feature representation of the conventional CNN reduces its ability to distinguish weak anomaly responses from complex masonry scattering. The standard U-Net improves the spatial continuity of the predictions because its encoder–decoder structure and skip connections preserve multi-scale information. Major anomaly regions are generally recovered more clearly than in the CNN results. However, the predicted boundaries remain relatively diffuse, and thin or weak structures are frequently over-smoothed. This behavior is particularly evident for delamination interfaces and narrow crack-like anomalies. The multi-input model benefits from the additional amplitude-envelope and gradient-magnitude channels. Compared with the standard U-Net, it produces fewer isolated false responses and improves the localization of several weak anomalies. The predicted regions are more consistent with the reference masks because the additional attributes increase the contrast between anomaly-related responses and the surrounding background. Nevertheless, some local discontinuities and over-smoothed regions remain, especially in cases containing strong clutter or spatially complex anomalies.

The proposed PG-AttUNet produces the most compact and spatially coherent predictions among the four models. Discrete voids are reconstructed with clearer boundaries, delamination interfaces retain greater lateral continuity, and the irregular crack is recovered with less background interference. For the moisture-affected model, the predicted region more closely preserves the overall extent and irregular morphology of the reference anomaly. In the composite case, multiple anomaly regions remain spatially distinguishable while scattered false detections are reduced.

These observations are consistent with the complementary roles of the three input representations and the attention-gated feature selection. The B-scan preserves waveform information, the envelope emphasizes reflection energy, and the gradient magnitude enhances local structural boundaries. The attention gates further reduce the transfer of clutter-dominated shallow features into the decoder.

Quantitative evaluation

The quantitative results are illustrated in Figure 7. The CNN model yields the highest MSE of 0.0186, the lowest PSNR of 17.31 dB, and the lowest SSIM of 0.781. These values are consistent with the fragmented predictions and numerous false responses observed in Figure 6. The standard U-Net reduces the MSE to 0.0124 and increases the PSNR and SSIM to 19.07 dB and 0.836, respectively. These improvements confirm that the encoder–decoder architecture provides more effective multi-scale spatial reconstruction than the conventional CNN. However, the remaining prediction errors reflect the blurred boundaries and loss of thin structures observed in the qualitative results. Introducing the physics-guided multi-channel input further improves the results. The multi-input model achieves an MSE of 0.0091, a PSNR of 20.41 dB, and an SSIM of 0.872. The decrease in MSE and increase in SSIM demonstrate that the amplitude-envelope and gradient-magnitude channels provide useful information beyond the B-scan. The proposed PG-AttUNet achieves the best performance for all three metrics, with an MSE of 0.0053, a PSNR of 22.76 dB, and an SSIM of 0.927.

Relative to the CNN baseline, these results correspond to a 71.5% reduction in MSE, a 31.5% increase in PSNR, and an 18.7% increase in SSIM, which are the percentage improvements indicated by the arrows in Figure 7. The lower MSE indicates improved pixel-level accuracy, whereas the higher PSNR and SSIM demonstrate better overall reconstruction quality and structural agreement with the reference anomaly masks. The quantitative improvements are consistent with the clearer boundaries, reduced false detections, and improved spatial continuity shown in Figure 6. Although the proposed method provides the best overall performance, small residual artifacts remain in regions affected by strong scattering or low signal amplitudes. Prediction accuracy also decreases in deeper regions where radar-wave attenuation reduces the distinction between anomaly-related responses and the surrounding background.

Field data acquisition and preprocessing

The field GPR data were acquired along the surface of a historic masonry wall using a ground-coupled GPR system equipped with a 400 MHz antenna. The measurement was performed in reflection profiling mode, with the antenna moved horizontally along the masonry surface while maintaining approximately constant coupling conditions. The investigated profile had a total length of approximately 2.0 m.

Each measured B-scan consisted of 1,030 spatial traces, and each trace contained 510 temporal samples. The recording time window was approximately 35 ns, corresponding to a temporal sampling interval of approximately 0.0688 ns. The spatial sampling interval was approximately 1.94 mm (0.00194 m) along the 2.0 m survey line. These relatively dense temporal and spatial sampling intervals were used to preserve waveform details and the lateral continuity of shallow reflections within the heterogeneous masonry structure.

The measured B-scan retained the complete field radar response, including direct-wave energy, reflections from brick–mortar interfaces, diffraction, multiple scattering, background clutter, and potential anomaly-related responses. No manual cropping or prior selection of suspected anomalous regions was performed. Before network prediction, the complete B-scan was normalized and used to calculate the corresponding amplitude-envelope and gradient-magnitude representations. The three representations retained the same spatial and temporal dimensions and were spatially aligned and stacked to form the three-channel input to the trained PG-AttUNet.

Field feature representations

Figure 8 shows the field GPR B-scan, amplitude envelope, and gradient magnitude obtained from the historic masonry structure. The B-scan contains a mixture of direct-wave energy, hyperbolic reflections, laterally continuous events, multiple scattering, and background clutter. Several strong responses are visible in the central and right portions of the profile, but their physical origin cannot be determined from the B-scan alone.

The amplitude envelope suppresses rapid waveform oscillations and highlights the principal reflected-energy distribution. A relatively continuous high-energy region is visible in the middle-right portion of the profile. This response may be associated with a local dielectric contrast caused by moisture accumulation, material degradation, an internal discontinuity, or a combination of these factors.

The gradient-magnitude representation emphasizes local changes in the radar wavefield. A vertically extended high-gradient zone is visible beneath the main high-energy response. This feature indicates a persistent spatial discontinuity and is compatible with a crack-like structure, a seepage-related pathway, or an irregular material interface. Additional weaker gradients are distributed throughout the profile and may reflect normal masonry heterogeneity, mortar joints, minor discontinuities, or measurement noise.

The agreement between the envelope and gradient representations provides useful physical support for interpreting the main anomalous region. However, neither representation alone provides direct evidence of the exact internal condition. The field data must therefore be evaluated using the combined spatial patterns of the B-scan, physical attributes, and predicted probability maps.

Comparison of field predictions

Figure 9 compares the anomaly-probability maps predicted by the four models. Because independent internal labels were unavailable for the measured structure, the field results were not evaluated against a pixel-level reference mask. Instead, the comparison focuses on spatial continuity, suppression of isolated responses, and consistency with the physically interpretable features shown in Figure 8.

The CNN result contains numerous isolated high-probability pixels and fragmented anomalous regions. Many of these responses do not correspond to continuous structures in either the amplitude-envelope or gradient-magnitude representations. The result therefore appears strongly affected by background clutter and local waveform variations.

The U-Net result improves spatial continuity and produces a dominant high-probability region in the upper-right portion of the profile. However, the prediction is excessively smooth, and some narrow or weak structures are not preserved. This suggests that the standard U-Net captures the general location of the dominant response but loses part of its detailed morphology.

The multi-input model produces a probability distribution that is more consistent with the high-energy and high-gradient regions observed in Figure 8. The main anomaly extends vertically from the shallow portion toward greater depth, and some secondary branches are also retained. Nevertheless, the result still contains fragmented responses in areas characterized by strong background interference.

The proposed PG-AttUNet generates a spatially continuous and compact anomaly pattern. The principal high-probability region extends from the shallow upper-right portion of the profile into a deeper and narrower structure. Its position and geometry are broadly consistent with the strong energy concentration observed in the amplitude envelope and the vertically extended feature in the gradient-magnitude representation.

Compared with the baseline models, PG-AttUNet produces fewer isolated background responses while retaining the dominant continuous anomalous structure. This behavior is consistent with the synthetic-data results, where the proposed method also showed improved spatial continuity and reduced false detections.

Interpretation of field anomalies

Figure 10 presents the probability map generated by PG-AttUNet together with an interpretation of the principal anomalous zones. The upper-right portion of the profile contains a relatively broad high-probability region. Its correspondence with strong reflected energy suggests a local zone of increased dielectric contrast. Potential explanations include moisture accumulation, material deterioration, internal separation, or localized changes in masonry composition. A narrow anomaly extends downward from the shallow high-probability region. This feature coincides with a vertically continuous gradient response and may represent a potential crack-propagation path or seepage-related channel. Its continuity from shallow to deeper portions of the profile suggests that it is unlikely to result solely from isolated random noise. Several weaker branches occur around the dominant vertical anomaly. These responses may be associated with subsidiary cracks, irregular mortar joints, interconnected pores, or small-scale variations in the masonry fabric. A lower-contrast response in the lower-left portion of the profile may indicate a locally modified or moisture-affected material zone, although the evidence for this interpretation is weaker. The field interpretation remains uncertain because no destructive inspection, core sampling, endoscopic observation, or independent geophysical measurement was available to verify the internal conditions directly. Accordingly, the predicted regions should be interpreted as probabilistic geophysical indications requiring further inspection rather than as definitive maps of individual cracks, voids, or seepage pathways.

This study developed a physics-guided deep learning framework for GPR imaging of hidden anomalies in heterogeneous historic masonry. The framework combines the B-scan, amplitude envelope, and gradient magnitude to provide complementary information on waveform characteristics, reflected-energy distribution, and local structural boundaries. These representations are processed using a physics-guided attention U-Net in which attention gates suppress irrelevant skip-connection features and retain spatial information associated with potential anomalies. The synthetic experiments demonstrate that the proposed PG-AttUNet provides more accurate and spatially coherent predictions than the conventional CNN, standard U-Net, and multi-input baseline. The proposed model achieved an MSE of 0.0053, a PSNR of 22.76 dB, and an SSIM of 0.927. It more effectively reconstructed discrete voids, laterally continuous delamination, narrow crack-like anomalies, irregular moisture-affected regions, and composite anomaly distributions. Application to field GPR data produced a dominant continuous anomaly extending from a shallow high-energy region toward greater depth. The predicted distribution was broadly consistent with the amplitude-envelope and gradient-magnitude responses and may indicate a crack- or seepage-related pathway accompanied by local moisture accumulation or material deterioration. However, because independent field labels were unavailable, the predicted zones should be interpreted as probabilistic indications rather than deterministic structural reconstructions. Overall, the results show that incorporating physically meaningful GPR attributes into an attention-based learning framework can improve the robustness, spatial continuity, and interpretability of anomaly imaging in heterogeneous masonry. Future work should focus on field-validated datasets, uncertainty estimation, multi-class anomaly identification, realistic antenna and material modeling, and extension from two-dimensional profiles to three-dimensional GPR imaging.