# Speckle Noise Removal in OCT Images via Wavelet Transform and DnCNN
## 2 Materials and Methods
### Denoising Convolutional Neural Network  
Denoising convolutional neural network (DnCNN) represents a deep convolutional neural network architecture specifically designed for image denoising tasks. This model leverages a deep supervised learning paradigm to adaptively characterize image noise distribution patterns, optimizing network parameters through backpropagation algorithms to achieve nonlinear end-to-end mapping from noisy to clean images. Under Gaussian noise conditions, DnCNN demonstrates superior denoising performance. The optical coherence tomography (OCT) images addressed in this study exhibit Poisson-distributed noise characteristics. To accommodate DnCNN's input requirements, we apply variance  
Figure 3: Schematic of SWT: (**a**) LL; (**b**) LH; (**c**) HL; and (**d**) HH.  
stabilizing transformation (VST) to preprocess raw images via square root operations, converting signal-dependent noise into additive Gaussian noise [24]. The adopted DnCNN network topology, as illustrated in Figure 4, comprises alternately stacked convolutional layers and batch normalization units, incorporating residual learning mechanisms with skip connections to enhance feature reuse capabilities and further improve denoising efficacy. The network depth is represented by B, with B = 25 employed in the experimental setup. The convolution kernel adopted in the architecture is of size \(3\times 3\times 64\).  
The network architecture was optimized using a residual learning paradigm, where the Mean Squared Error (MSE) loss function quantified the reconstruction fidelity between paired noisy-clean OCT image domains. This objective function facilitated gradient-efficient backpropagation through identity mapping connections, enabling effective minimization of structural discrepancies.  
All experimental datasets comprised B-scan optical coherence tomography (OCT) images with dimensions of 3 mm \(\times\) 3 mm, yielding a resolution of 640 \(\times\) 304 pixels. The training cohort was sourced from the Nanjing University repository, containing 115,520 OCT images acquired from 380 subjects. This cohort included 49 age-related macular degeneration (AMD) cases, 16 choroidal neovascularization (CNV) cases, 64 diabetic retinopathy (DR) cases, and 251 healthy controls. For model validation, an independent dataset was utilized, consisting of 10,640 OCT images obtained from 35 subjects at Shanxi Eye Hospital, comprising 5 AMD cases, 7 CNV cases, 16 DR cases, and 7 healthy controls.  
The training pipeline of the proposed DnCNN architecture is illustrated in Figure 5, incorporating a multi-resolution feature extraction strategy. Each OCT image from the dataset underwent DWT decomposition, yielding four sub-band components: LL, LH, HL, and HH. The LL sub-band, representing coarse-scale structural information, subsequently underwent SWT decomposition to generate four additional frequency-specific representations.  
This multiscale decomposition enabled parallel channel processing, where each wavelet-derived component (4 DWT sub-bands + 4 SWT sub-bands) was independently fed into the denoising network. All channels adopted identical network configurations, ensuring consistent feature extraction across spatial frequency domains. The training objective minimized the MSE loss between network outputs and corresponding noise-free ground truths, with gradient updates propagated through residual connections to preserve low-frequency contextual information.  
To enhance convergence stability, the Adam optimizer (\(\beta_{1}\) = 0.9, \(\beta_{2}\) = 0.999) was employed with an initial learning rate of 1 \(\times\) 10\({}^{-4}\), while batch normalization layers regulated internal covariate shift during the 50-epoch training regimen.  
Figure 4: The architecture of the proposed DnCNN network.