NGQR: A Novel Generalized Quantum Image Representation

To address the size limitations of existing quantum image models in terms of accurate image representation, as well as inaccurate image operation and retrieval, we propose a Novel Generalized Quantum Image Representation (NGQR) for images of arbitrary size and type. For generalizing the size model, we first propose the Perception-Aided Encoding (PE) method to perceive the target qubits in the quantum information. Based on PE, we propose the quantum image representation PE-NGQR, which accurately ignores redundant information thereby targeting valid pixels for operations and retrieval. Then, to accurately represent the needed pixel information without redundancy, we propose the Coherent-Size Encoding (CE) method. The CE can encode an arbitrary number of quantum states. Based on CE, we propose CE-NGQR, a quantum image model capable of accurate image representation, processing and retrieval. Specifically, we describe in detail the concept, representation and quantum circuits of NGQR. We provide detailed quantum circuits and simulations of NGQR-based operations and geometric transformations. Moreover, NGQR enables flexible quantum image scaling. We illustrate the complementarity of the proposed PE-NGQR and CE-NGQR through complexity simulations and clarify the respective applicability scenarios. Finally, comparisons and analyses with existing quantum image models demonstrate the versatility and flexibility advantages of NGQR.