Implementing bilinear interpolation with quantum images

A bilinear interpolation technique is proposed for flexible representations of quantum images (FRQIs). In this process, several quantum modules were developed, including assignment, increment, and quarter modules, for use in an interpolation circuit. The network structure of these circuits, capable of both up-sampling and down-sampling FRQIs, was investigated as part of the study. Additionally, the proposed method was verified using a series of simulation experiments in which test samples were enlarged and reduced, for comparison with nearest-neighbor interpolation. The up-scaled images produced using the proposed technique were of higher quality than those produced using nearest-neighbor interpolation, as measured using the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM). Finally, with the extension of the FRQI model from square to rectangular shapes, the proposed algorithm is used to process rectangular FRQIs with special and arbitrary sizes.