The traditional image denoising methods could effectively remove the noise. But the useful information in the detail abundant areas would be thrown off, and the edge appears mistiness. The search for efficient image denoising methods is still a valid challenge in image processing. This paper proposes a method for removing noise with keeping image detail in smoothness areas and detail abundant areas. The main focus of this paper is to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms. A bivariate rational interpolation with parameters is used in the algorithm. An interpolation surface is constructed using an image data as the interpolation data. According to the maximum and minimum membrane energy value of the interpolation surface, the noise pixel is detected. If it is a noise point, the value is replaced by the rank-ordered mean of the filter window and the membrane energy during noise removal. The experimental results demonstrate that the proposed method outperforms other conventional methods and recently proposed methods in reducing noise and retaining details.