基于能量泛函和视觉特性的全变分图像降噪模型

目的 基于能量泛函的全变分图像复原模型(ROF)为偏微分方程在图像处理上的应用开辟了一个新的研究领域。针对ROF模型存在的缺陷，很多学者提出了改进的模型和算法，并取得了一定的效果。基于能量泛函和视觉特性提出一种全变分图像降噪模型。方法 首先利用偏微分方程比较原理证明了该模型解的整体存在性，并利用变分原理给出了该模型的Euler-Lagrange方程；在数值计算时，选用人工时间演算法和有限差分方法，对数值近似解的离散形式进行了图像降噪matlab实验；最后利用峰值信噪比和平均结构相似度两个指标进行了降噪质量评价。结果 从实验数据上来分析，本文的模型在峰值信噪比上都有0.5~1 dB的提高，结构相似度有0.05~0.3的改进。结论 从降噪效果上分析，基于能量泛函和视觉特性的全变分图像降噪模型能够在降噪的同时，保持良好的边缘和纹理特征，优于其他改进的全变分降噪模型。

TV image denoising model based on energy functionals and HVS

Objective The total variation image debluring model (ROF) based on energy functional opened up a new area of research on image processing, particularly on the application of partial differential equations. The defects of the ROF model have prompted many scholars to study the improved model and its algorithm. These scholars have achieved good Results. This study presents a TV image denoising model based on energy functionals and HVS.Method The existence of solutions for the denoising model in this paper is proven by using the comparison principle of the partial differential equation, and the Euler-Lagrange equation of the model is given using the variation principle. In terms of the numerical calculation of the model, this study discusses the discrete form of numerical approximation solution through artificial time algorithm, finite difference Methods, and numerous image denoising MATLAB experiments. Finally, the two indexes of noise quality are evaluated based on the peak signal-to-noise ratio (PSNR) and mean structural similarity (MSSIM).Result The (0.5~1) dB PSNR and the (0.05~0.3) MSSIM present an improvement based on the experimental data and Results.Conclusion From the analysis of denoising, the TV image denoising model based on energy functionals and HVS can maintain the image edge and texture features and is thus superior to conventional TV denoising models.