基于变分模型的混合噪声去噪方法

Study on mixed noise removal by the total variation method

针对现有降噪方法仅满足单一噪声的去除需要,无法解决多种混合噪声的去噪问题的缺陷,提出一种加权混合噪声模型,建立其能量泛函表达式,利用变分法获得其欧拉-拉格朗日方程并给出其显式差分数值解法。通过对显式差分数值方法进行改进,不仅可以提高该模型数值算法的速度和稳定性,而且可以在一定程度上避免降噪后图像的阶梯效应。实验结果表明,加权混合噪声去噪算法在去除混合噪声的同时更好地保留了图像的细节信息,其降噪性能相比现有方法能够有一定程度的改善。

The present noise reduction methods can only satisfy the need for the single noise re- moval and cannot solve the de-noising problem of the various mixed noise. A weighted mixed noise model was proposed. In this model, the energy functional expression of the model was es- tablished. The Euler-Lagrange equation of the model was obtained by the variation method, and the numerical solution was given by the explicit difference scheme. By modifying the explicit difference method, this model can not only enhance the speed and the stability of numerical algo- rithm, but also avoid the staircase effect of the image de-noising to a certain degree. The experi- mental results showed that this model can effectively remove mixture noise while the more details of image edge could still be preserved well, and that the noise reduction performance can be im- proved to a certain degree compared to the existing methods.