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Adaptive Gaussian filter (AGF) is a recently developed switching filter to remove salt and pepper noise. AGF first directly identifies pixels of gray levels 0 and 255 as noise pixels, and then only restored noise pixels using a Gaussian filter with adaptive variance based on the estimated noise density. AGF usually achieves better denoising effect in comparison with other filters. However, AGF still fails to obtain good denoising effect on images with noise-free pixels of gray levels 0 and 255, due to its severe false alarm in its noise detection stage. To alleviate this issue, a modified version of AGF is proposed in this paper. Specifically, the proposed filter first performs noise detection via an image block based noise density estimation and sequential noise density guided rectification on the noise detection result of AGF. Then, a modified Gaussian filter with adaptive variance and window size is used to restore the detected noise pixels. The proposed filter has been extensively evaluated on two representative grayscale images and the Berkeley image dataset BSDS300 with 300 images. Experimental results showed that the proposed filter achieved better denoising effect over the state-of-the-art filters, especially on images with noise-free pixels of gray levels 0 and 255.