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

Abstract

In quantum image processing, the scaling techniques have undergone extensive research, representing 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 approach. By integrating the NEQR representation with an enhanced bilinear interpolation from OpenCV, the central misalignment is effectively rectified. In addition, the algorithm steps for quantum image scaling-up and scaling-down have been optimized based on the properties of optimization algorithms and quantum computing, facilitating easier implementation in quantum circuits. Furthermore, simpler quantum modules and quantum convolution algorithms have been introduced to reduce circuit complexity. Through a series of simulation experiments and complexity analyses, it has been demonstrated that our method achieves exponential acceleration compared to the initial bilinear interpolation method. It also resolves the issues of central misalignment in image scaling and algorithm degradation in integer multiple image scaling-down. Additionally, our method features lower circuit complexity and reduced qubit usage.