Quantum implementation of bilinear interpolation algorithm based on NEQR and center alignment

Abstract In the field of quantum image processing, scaling techniques have been extensively studied as a critical subfield. Predominantly, these techniques leverage bilinear interpolation method. However, the current quantum bilinear interpolation algorithm remains in its initial version, resulting in a significant flaw: the centers of the source image and the interpolated image are misaligned. This flaw not only leads to results identical to nearest neighbor interpolation during integer multiple image scaling-down but also causes excessive qubit usage. To tackle these issues, our study introduces an innovative bilinear interpolation method with the following key advancements. Firstly, by integrating the NEQR representation with an enhanced bilinear interpolation from OpenCV, the central misalignment is effectively rectified. Secondly, resolving the central misalignment enables our method to prevent the degradation to nearest neighbor interpolation during integer multiple image reduction. Finally, based on the characteristics of optimization algorithms and quantum computing, along with simpler quantum modules and quantum convolution algorithms, the steps of the quantum image scaling algorithm have been optimized to reduce circuit complexity. Through a series of simulation experiments and complexity analyses, it has been demonstrated that our method, compared to the initial bilinear interpolation method, exhibits lower circuit complexity and significantly reduces qubit usage.