Aiming at the problems of discontinuity

high-order non-conductive and signal oscillation of traditional threshold functions

an image de-noising method based on improved threshold function is proposed. The method is continuous and high-order derivative in the definition domain. The expression structure is simple and easy to calculate. The deviation between the estimated wavelet coefficients and the wavelet coefficients of noise pollution is controlled by adjusting the parameters

and the image blurring problem is solved. Simulated de-noising by adopting the traditional hard threshold

the soft threshold

and semi-soft threshold method combined with the proposed method. At the same time

the four kinds of de-noising effects are compared and analyzed from the subjective and objective perspectives. Experimental results show that the improved threshold function method not only can effectively remove Gaussian noise of different degrees

but also can better preserve the edge and detail information of the image. This method is high in peak signal to noise ratio（ PSNR） and mean absolute error（ MAE）. Denoising performance is also significantly better than other algorithms.