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

To reduce image noise, we propose a novel image filter based on stepwise ratio grey model (SGM). The basic theory and the method of stepwise ratio grey prediction model are introduced first. The new filter makes use of neighborhoods around each noisy pixel to predict its intensity value and reflects the dynamics of stepwise ratio. The experimental results show that the proposed method, compared with the median filter and GM(1, 1) model, improves the effect of the removal of impulse noise, such as salt & pepper noise. The improved algorithm 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. Therefore the proposed method is practicable.