# Speckle Noise Removal in OCT Images via Wavelet Transform and DnCNN
## 1 Introduction  
Optical coherence tomography (OCT) [1] represents a cutting-edge, non-invasive imaging technology that harnesses the interference of reflected light to produce high-resolution two-dimensional or three-dimensional images. This technique enables an in-depth examination of tissue microstructures and facilitates the detection of subtle structural and laminar alterations, thereby establishing its prominence across multiple medical domains, particularly in ophthalmology. With the widespread application of OCT, the quality of OCT images has emerged as a significant factor influencing diagnostic effectiveness. Although OCT systems are capable of providing high-resolution structural information during imaging, the image quality is often compromised by the presence of speckle noise [2; 3]. To enhance the visualization of OCT images and extract more precise diagnostic information, image denoising has become a crucial task in post-imaging processing [4; 5; 6; 7; 8]. Traditional image denoising methods [9], such as the least squares method [10] and median filtering, have been extensively applied to denoise OCT images. While these methods can effectively reduce speckle noise to some extent, they often result in the loss of image details. Another common denoising approach is Anisotropic Diffusion [3], which, while preserving certain edge information while removing noise, often falls short when dealing with high-noise OCT data, failing to meet the requirements for high-quality image restorations. In comparison, wavelet transform methods [11] have demonstrated superior performances in image denoising, effectively distinguishing between noise and signal components through a multiscale processing approach. Recent advancements in wavelet-based denoising have focused on incorporating adaptive mechanisms to address heterogeneous noise characteristics in medical imagery [12; 13]. [PERSON] et al. introduced a noise-adaptive wavelet thresholding (NAWT) framework that leverages a spectral discrepancy analysis across wavelet sub-bands, demonstrating performance gains in the ultrasonic tissue characterization [14]. Building upon multi-resolution analysis foundations, [PERSON] et al. proposed a hybrid threshold function combining hard and soft thresholding paradigms, achieving an improved edge preservation through spatially variant coefficient manipulation [15]. For optical coherence tomography (OCT) applications, [PERSON] et al. developed a particle swarm optimization (PSO)-driven threshold selection strategy, incorporating local texture descriptors (variance/gradient metrics) to enable context-aware noise suppression in retinal layer segmentation tasks [16]. These methodologies collectively advance wavelet denoising through two principal innovations: the implementation of spatially adaptive threshold modulation mechanisms that retain critical diagnostic features while attenuating stochastic artifacts and the integration of local statistical descriptors, such as inter-scale correlation and directional variance, into multiscale processing pipelines. Notably, the PSO-OCT framework achieved a 12.7% improvement in the SNR over conventional thresholding methods through a dynamic parameter optimization across 256 \(\times\) 256 pixel regions. Concurrently, hybrid architectures combining wavelet transforms with deep learning have emerged as promising alternatives [17; 18; 19; 20]. [PERSON] et al. demonstrated a convolutional neural network (CNN)-augmented wavelet denoiser that outperformed traditional methods by 8.2 dB in PSNR metrics through the joint optimization of thresholding matrices and feature extraction kernels [21]. More recently, residual learning paradigms integrated with Stationary Wavelet Transforms (SWTs) have shown particular efficacy in preserving microstructural details critical for an OCT diagnosis [22].