分数阶偏微分方程在图像去噪中的应用研究

项目名称： 分数阶偏微分方程在图像去噪中的应用研究

项目编号： No.61201438

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 黄果

作者单位： 乐山师范学院

项目金额： 24万元

中文摘要： 为了在去噪的同时更多地保留图像的细节信息，本项目拟将分数阶微积分理论和梯度下降流有效结合，提出分数阶梯度下降流的概念，并尝试证明能量泛函的分数阶梯度下降流在一定微分阶次范围内是收敛的。其次，本项目拟利用分数阶微分掩模算子来实现基于空间分数阶偏微分方程的图像去噪模型的数值计算，并引入以分数阶梯度模值为参数的边缘停止函数来控制图像扩散强度。在此基础上，本项目拟将时间因素引入到改进的基于空间分数阶偏微分方程的图像去噪模型中，从而尝试构建基于时间-空间分数阶偏微分方程的图像去噪模型，该模型拟实现在时间方向上和空间平面内的同步去噪，不仅可以提高去噪后图像的信噪比，而且可以大幅减少图像获得最大信噪比所需要的迭代次数。

中文关键词： 分数阶微积分；分数阶偏微分方程；分数阶梯度；图像去噪；

英文摘要： In order to preserve more image details information while image denoising, the concept of fractional-order gradient descent flow is proposed by combining fractional calculus and gradient descent flow, and try to prove that the fractional-order gradient descent flow of energy function is convergent within a certain range of differential order. Secondly, the numerical of denoising model based on space fractional partial equation is achieved by using fractional differential mask operator, and it could control the intensity of image diffusion by introducing the edge stopping function including the parameters of fractional grads modulus. On this basis, the denoising model based on time-space fractional partial equations is constructed by adding time factor to the improved image denoising model based on space fractional partial equations. The denoising model proposed in this project should achieve synchronously denoising in the directions of time and space, so it appropriately increases the signal-to-noise ratio of image and significantly reduces the iteration number under the conditions that the signal-to-noise ratio of denoising image getting the maximum.

英文关键词： fractional calculus；fractional-order partial differential equations；fractional-order gradient；image denoising；