Enhancing quality and removing noise during preprocessing is one of the most critical steps in image processing. X-ray images are created by photons colliding with atoms and the variation in scattered noise absorption. This noise leads to a deterioration in the graph's medical quality and, at times, results in repetition, thereby increasing the patient's effective dose. One of the most critical challenges in this area has consistently been lowering the image noise. Techniques like BM3d, low-pass filters, and Autoencoder have taken this step. Owing to their structural design and high rate of repetition, neural networks employing diverse architectures have, over the past decade, achieved noise reduction with satisfactory outcomes, surpassing the traditional BM3D and low-pass filters. The combination of the Hankel matrix with neural networks represents one of these configurations. The Hankel matrix aims to identify a local circle by separating individual values into local and non-local components, utilizing a non-local matrix. A non-local matrix can be created using the wave or DCT. This paper suggests integrating the waveform with the Daubechies (D4) wavelet due to its higher energy concentration and employs the u-Net neural network architecture, which incorporates the waveform exclusively at each stage. The outcomes were evaluated using the PSNR and SSIM criteria, and the outcomes were verified by using various waves. The effectiveness of a one-wave network has increased from 0.5% to 1.2%, according to studies done on other datasets.

翻译：提高图像质量与去除预处理噪声是图像处理中最关键的步骤之一。X射线图像由光子与原子碰撞以及散射噪声吸收的变化生成。这种噪声会导致图像医学质量下降，有时甚至需重复拍摄，从而增加患者的有效辐射剂量。该领域最关键的挑战之一始终是降低图像噪声。BM3D、低通滤波器和自编码器等技术已在此领域取得进展。由于神经网络在结构设计和重复率方面的优势，采用不同架构的神经网络在过去十年中实现了优于传统BM3D和低通滤波器的去噪效果。汉克尔矩阵与神经网络的组合正是此类构型之一。汉克尔矩阵旨在通过将单个值分离为局部和非局部分量，利用非局部矩阵识别局部圆域。非局部矩阵可通过小波或DCT生成。本文建议将波形与能量集中度更高的Daubechies（D4）小波进行集成，并采用u-Net神经网络架构——该架构仅在每阶段嵌入波形。通过PSNR和SSIM标准评估结果，并利用多种波形验证性能。基于不同数据集的实验表明，单波形网络的有效性提升了0.5%至1.2%。