Stepwise ratio GM (1,1) model for image denoising

Purpose The purpose of this paper is to construct a novel grey filter model for image denoising and to solve the problems which exist in the image denoising filter method, in which the true intensity value of each noisy pixel cannot be predicted better. Design/methodology/approach Based on the definition of stepwise, the defects of traditional grey prediction models are found. A new grey filter model, named grey stepwise prediction model, is proposed. The new filter model for the image denoising is based on each noisy pixel's neighborhoods stepwise, which is the eight pixels around the noisy pixel, to predict its intensity value and to solve the problems which exist in the image denoising filter method. Findings The experiment results show that the improved filter model can effectively eliminate image noise, preserve the image's details and edges, increase SNR (signal‐to‐noise ratio) as well as PSNR (peak signal‐to‐noise ratio), reduce MSE (mean square error) and MAE (mean absolute error), and significantly improve the image's visual effect. Practical implications The new filter method exposed in the paper can be used to 8‐bit gray‐scale image denoising. The method can also be used to binary image denoising. Originality/value The paper succeeds in constructing a novel filter method for image denoding, and it is undoubtedly a new development in image recovery algorithm and grey systems theory.