QGIP: A Framework Bridging Quantum Grayscale Image Processing and Applications

Quantum computing offers parallel processing capabilities and resource-saving advantages, particularly useful for managing expansive datasets and complex image processing tasks. Grayscale images, being the simplest single-channel image mode, are frequently employed in artificial intelligence training. Before actual image applications, various image processing operations are typically required. However, the restoration of a grayscale image of dimensions 2ⁿ × 2ⁿ after a series of linear transformations poses a challenge. Existing methods typically involve finding the inverse of the most recent linear transformation or re-encoding the image followed by repeated operations until the final transformation, resulting in excessive computational overhead and disconnection from subsequent quantum grayscale image applications. To address this issue, we propose a universal quantum linear restoration algorithm for grayscale image, denoted as QLR, which effectively bridges the stages of linear transformation and subsequent image applications. QLR reduces the time complexity from O(2ⁿ) to O(n) compared to classical counterpart. Building upon the QLR algorithm, we further propose two quantum resource-optimized compression methods for optional lossless image storage. Combining with other quantum algorithms and techniques, we design a framework (QGIP) aimed at bridging the processes of quantum grayscale image processing and applications. Experiments simulated on the IBM Quantum platform validate the correctness and efficiency of our proposal.