提出一种新自适应去噪函数。与经典的硬阈值函数与软阈值函数相比,此函数具有明显优点。首先,此函数表达式简单易于计算,连续并有无穷阶导数,便于进行各种数学处理;其次,本文证明了新函数具有收敛性、连续可导性及自适应性,为信号的自适应去噪提供了新的方法。仿真结果表明新函数不仅能有效去除噪声,而且比两种经典的阈值函数有更高的信噪比和更好的视觉效果,去噪后图像相对硬阈值函数去噪图像较光滑,相对软阈值函数去噪图像则更多地保留了图像边缘等局部特征,同时其均方误差最小,优于经典的两种阈值函数。

In this paper we introduce a new function for image denoising. The new function is simple and continuous. It obtains some advantages from both: the hard-thresholding function and the soft-thresholding function. It overcomes the shortcoming that there is an invariable dispersion between the estimated wavelet coefficients and decomposed wavelet coefficients of the soft-thresholding method. At the same time, this function overcomes the shortcoming of the hard-thresholding method with discontinuous functions. We proof that the new function satisfies the shrinkage condition and has infinite rank continuous derivative. At the same time, it has adaptive character and is suitable for various mathematical processing. These advantages make it possible to construct an adaptive algorithm for image denoising. At last, several numerical experiments show that the proposed new function is very effective and predominant. It gives better performance both in terms of PSNR and in visual quality. Our function can preserve more significant information of original images like edges and details than the soft-thresholding function. At the same time, the images denoised by our function are smoother than those denoised by the hard-thresholding function. It also gives a better MSE performance than two typical methods.