An anti-aliasing filtering of quantum images in spatial domain using a pyramid structure

As a part of quantum image processing, quantum image filtering is a crucial technology in the development of quantum computing. Low-pass filtering can effectively achieve anti-aliasing effects on images. Currently, most quantum image filterings are based on classical domains and grayscale images, and there are relatively fewer studies on anti-aliasing in the quantum domain. This paper proposes a scheme for anti-aliasing filtering based on quantum grayscale and color image scaling in the spatial domain. It achieves the effect of anti-aliasing filtering on quantum images during the scaling process.First, we use the novel enhanced quantum representation(NEQR) and the improved quantum representation of color images(INCQI) to represent classical images. Since aliasing phenomena are more pronounced when images are scaled down, this paper focuses only on the anti-aliasing effects in the case of reduction. Subsequently, we perform anti-aliasing filtering on the quantum representation of the original image and then use bilinear interpolation to scale down the image, achieving the anti-aliasing effect. The constructed pyramid model is then used to select an appropriate image for upscaling to the original image size. Finally, the complexity of the circuit is analyzed. Compared to the images experiencing aliasing effects solely due to scaling, applying anti-aliasing filtering to the images results in smoother and clearer outputs. Additionally, the anti-aliasing filtering allows for manual intervention to select the desired level of image smoothness.