## 5 Discussion  
WPD-Net, a deep learning architecture has been proposed for denoising wrapped-phase images under severe speckle, Gaussian, and mixed noise conditions. The network employs multi-scale feature extraction and attention mechanisms to focus on relevant spatial and channel details while maintaining phase continuity. Combined with a dynamic hybrid loss function, these design choices enable robust noise suppression while preserving structural integrity.  
The experiments conducted with both synthetic and real datasets confirm that WPD-Net consistently delivers high-quality denoising results. This not only enhances reconstruction accuracy but also ensures reliable inputs for downstream tasks such as phase unwrapping. While many existing deep learning-based phase unwrapping methods attempt to jointly denoise and unwrap phase images, they typically require large and diverse training datasets [40; 41; 42], along with long training durations--often exceeding 10 h [39]. Moreover, their performance can deteriorate significantly when exposed to complex mixed noise. In contrast, our two-stage approach--first applying WPD-Net for denoising, followed by a simple unwrapping algorithm--offers better adaptability, lower computational cost, and faster inference. As a lightweight model with significantly fewer parameters than conventional joint models, WPD-Net reduces training time to under two hours and achieves real-time inference (21.19 ms per image), making it well-suited for practical applications where both accuracy and speed are critical.  
To visualize the effectiveness of this workflow, 3D surface plots of unwrapped-phase images are shown in Figure 12. For both the acrylic and PDMS samples used in Figure 10(a-1,a-2), the combination of WPD-Net and a basic 2D unwrapping method produces clean and coherent 3D surfaces, comparable to the outputs from recent end-to-end phase unwrapping networks like DenSFA-PU [39] and U\({}^{2}\)-Net [42]. These results highlight the practical value of separating denoising and unwrapping stages when using a highly capable denoising model like WPD-Net. While we demonstrated WPD-Net's ability to produce visually accurate unwrapped-phase results, a detailed quantitative assessment of the unwrapping accuracy using different denoising methods was not performed, as the primary focus of this study was on wrapped-phase denoising.  
Figure 12: 3D surface plots of the phase images unwrapped from the inputs shown in Figure 10(a-1,a-2). For the acrylic sample: (**a-1**) result obtained using WPD-Net denoising followed by a simple 2D phase unwrapping algorithm, (**a-2**) result from DenSFA-PU, and (**a-3**) result from U\({}^{2}\)-Net. For the PDMS sample: (**b-1**) result from WPD-Net with basic unwrapping, (**b-2**) result from DenSFA-PU, and (**b-3**) result from U\({}^{2}\)-Net result.  
Nevertheless, a limitation remains under extreme noise conditions (SNR < 0 dB). Although WPD-Net performs robustly at an SNR of 0 dB, its performance may deteriorate when the noise power exceeds the signal, limiting the network's ability to recover meaningful information. In future work, we aim to address this challenge by incorporating training strategies that account for temporal dynamics or large missing regions, thereby improving both robustness and generalization. Additionally, we plan to introduce phase unwrapping accuracy metrics, such as NRMSE or unwrapping error rate, to quantitatively evaluate the effectiveness of WPD-Net-enabled workflows compared to those using other denoising methods.