Asymmetric scaling scheme over the two dimensions of a quantum image

Although quantum image scaling algorithms have been widely studied in recent years, almost all of them require the quantum image to be enlarged or reduced simultaneously in the horizontal and vertical directions. However, the scaling schemes that enlarge the quantum image in one direction and shrink it in the other direction are rarely involved. In this paper, a quantum image scaling scheme based on the extension of the bilinear interpolation method is proposed to achieve asymmetric scaling over the two dimensions of a quantum image for the first time. Firstly, the improved novel-enhanced quantum representation of digital images (INEQR) is employed to represent a \( 2^{{n_{1} }} \times 2^{{n_{2} }} \) quantum image, and the bilinear interpolation is improved to use two adjacent pixels in the original image for interpolation. Then, the concrete circuits for the asymmetric scaling of quantum images are designed. Finally, the simulation results are given, and the complexity of the quantum circuits and the peak signal-to-noise ratio (PSNR) are used to quantitatively compare with the similar scheme proposed in another paper. The results show that the proposed scheme has lower computational complexity and better scaling effect than another scheme.