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.

提出了一种双线性插值技术，用于灵活表示量子图像 (FRQI)。在这个过程中，开发了几个量子模块，包括赋值、增量和四分之一模块，用于插值电路。作为研究的一部分，研究了能够对 FRQI 进行上采样和下采样的这些电路的网络结构。此外，使用一系列模拟实验验证了所提出的方法，其中测试样本被放大和缩小，以与最近邻插值进行比较。使用所提出的技术生成的放大图像比使用最近邻插值生成的图像质量更高，这是使用峰值信噪比 (PSNR) 和结构相似性指数 (SSIM) 测量的。最后，