Abstract: An improved iterating algorithm was proposed to eliminate the speckles preserved by the local curvaturebased model as geometrical characteristic. It utilized the local curvature coupling 3 channels as the regularizing term，then detected speckles by using local statistics values. The relaxed median filter was introduced to suppress these speckles. Numerical experiments using images of different features were carried out and the evolution of the values of the peak signal to noise ratio(PSNR) was analyzed. The results show that this algorithm can accelerate the progress of evolution and eliminate the speckles while protecting the image structure information. The value of the PSNR increases by 2.47%, and the iterations decrease by 93.66%.