Abstract:

The effect of the existing Total Variation (TV) method for image denoising is not ideal, and it is not good at keeping the characteristics of image edge and texture details. A new method of image denoising based on rational-order differential was proposed in this paper. First, the advantages and disadvantages of the present image denoising methods of TV and fractional differential were discussed in detail, respectively. Then, combining the model of TV with fractional differential theory, the new method of image denoising was obtained, and a rational differential mask in eight directions was drawn. The experimental results demonstrate that compared with the existing denoising methods, Signal Noise Ratio (SNR) is increased about 2 percents, and the method retains effectively the advantages of integer and fractional differential methods, respectively. In aspects of improving significantly high frequency of image and keeping effectively the details of image texture, it is also an effective, superior image denoising method. Therefore, it is an effective method for edge detection.

Key words: Image denoising, Total variation, Rational-order differential, Texture detail, Objective evaluation index

摘要：

针对现有的全变分(TV)去噪方法效果不太理想，在去噪的同时不能较好地保持图像的边缘和纹理细节，提出了一种基于有理数阶微分的图像去噪新方法。首先详细地讨论了现有的全变分去噪方法和分数阶微分去噪方法各自的优缺点；然后将全变分去噪模型与分数阶微分理论相结合，获得有理数阶微分图像去噪新模型，并推导了相应的有理数阶微分模板。实验结果表明：与改进前的方法相比，信噪比(SNR)提高了接近2个百分点，较好地传承了全变分去噪方法对图像高频部分大幅改善及分数阶微分去噪方法能够很好地保留图像纹理细节的优点，是一种有效的图像去噪方法。

关键词: 图像去噪, 全变分, 有理数阶微分, 纹理细节, 客观评价指标