Quantum Edge Detection and Convolution Using Paired Transform-Based Image Representation

Classical edge detection algorithms often struggle to process large, high-resolution image datasets efficiently. Quantum image processing offers a promising alternative, but current implementations face significant challenges, such as time-consuming data acquisition, complex device requirements, and limited real-time processing capabilities. This work presents a novel paired transform-based quantum representation for efficient image processing. This representation enables the parallelization of convolution operations, simplifies gradient calculations, and facilitates the processing of one-dimensional and two-dimensional signals. We demonstrate that our approach achieves improved processing speed compared to classical methods while maintaining comparable accuracy. The successful implementation of real-world images highlights the potential of this research for large-scale quantum image processing, architecture-specific optimizations, and applications beyond edge detection.