Quantum color image median filtering in the spatial domain: theory and experiment

Median filters are widely used to smooth data in image processing tasks and eliminate noise with extremely large or small magnitude. Thus, this paper proposes a median filtering method for quantum color images in the spatial domain, with the corresponding quantum circuit simulated on IBM the Quantum Experience (IBM Q) platform. In our technique, first, we improve the quantum color image storage module and adopt nine quantum color images to represent the core image (image to be processed) and its 8-neighborhoods. Then, a quantum comparator and a quantum control swap operation with low time complexity are employed to design the quantum median calculation module. Finally, we design the quantum circuit for color image median filtering, simulated on the IBM Q platform. Compared with existing methods, the proposed method’s time complexity is significantly reduced from \(O({q^2})\) to O(q) and the auxiliary qubit is reduced from O(q) to O(1). The developed scheme provides the framework for encoding the neighborhood information of pixels in supplementary images and reduces the auxiliary qubits and time complexity, demonstrating the potential of quantum image processing for highly efficient image and video processing tasks in the big data era.