Denoising of two-dimensional fractional Fourier transform images based on windowing
基于加窗的二维分数阶傅里叶变换图像去噪

摘要

针对图像处理技术在滤波过程中对图像造成的细节和边缘的信息损失，提出一种基于加窗的二维分数阶傅里叶变换的图像去噪方法。首先，运用窗函数对图像的纹理细节和边缘进行保护；其次，通过二维分数阶傅里叶变换将加窗后的图像转换成频谱图，将频谱能量最大作为最佳的变换的阶次选取的依据，利用二维搜索算法寻找最佳阶次；然后在分数域中进行低通滤波处理，并与三种传统去噪算法进行实验对比；最后通过峰值信噪比（PSNR）验证图像去噪效果，同时采用Soble算子进行边缘检测来评估边缘保留能力。实验结果表明，使用加窗的二维分数阶傅里叶变换处理图像对复杂的细节信息和纹理特征保留能力更好，提高了图像的视觉质量和清晰度。

Abstract

In this paper, two-dimensional windowed fractional Fourier transform for image denoising is proposed to address the loss of detail and edge information, which is caused by image processing technology in filtering process. Firstly, window function is used to protect the texture details and edges of the image. Secondly, the spectrum of the windowed image is presented by two-dimensional fractional Fourier transform, and obtain the maximum spectral energy by the selecting the optimal transformation order, which is given by the two-dimensional search algorithm. Thirdly, we compare proposed denoising algorithm with three traditional ones through experiments. the denoising effect of the image is verified through Peak Signal to Noise Ratio (PSNR), and the Soble operator is used for edge detection to evaluate the edge preservation ability. The experimental results show that windowed two-dimensional fractional Fourier transform for image processing has better retention ability for complex detail information and texture features, and improves the visual quality and clarity of the image.