Abstract: Based on the principle of Gyrator transform, the self-imaging effect, i.e., the Talbot effect, was investigated firstly. The condition under which the Gyrator transform Talbot effect can occur was given, and the difference between the Talbot effect mentioned in this paper and the traditional Talbot effect was found the Talbot angle was not fixed, the distribution of the angles was not linear, and the fractional Gyrator transform Talbot effect could not obtain through fractionalizing the Talbot angle. Secondly, noise reduction in image processing based on Gyrator transform was also discussed in the paper. It was found that the Gyrator transform could not only reduce the hyperbolic noise efficiently, but also can reduce the-kind noise that brings hyperbolic information efficiently. At last, the shortcoming of the study and follow-up investigations were pointed out. The research in this paper can help people understand Gyrator transform deeply, also develop the self-imaging and noise reduction techniques.