Quantum image mid-point filter

Mid-point filter is an order statistic filter which cannot be realized in the frequency domain. It is used for de-noising Gaussian noise effectively. In this paper, a new method for quantum realization mid-point filter in the spatial domain is proposed. An enhanced method for preparing multiple copies of the same image is also proposed. The modular design of the quantum circuit was utilized with an articulation on reducing the number of ancillary qubits. In this work, we present the quantum circuit for the three basic modules (cyclic shift, swap and division by two) and four composite modules (full adder, comparator, sort and maximum–minimum extraction). Also, the enhanced quantum preparation of multiple copies of an image is introduced. Moreover, the design of maximum–minimum extraction is modified to adapt our quantum circuit design. Finally, the complete quantum circuit which implements the mid-point filtering task is constructed and the results of several simulation experiments with different noise patterns are presented on some grayscale images. Apparently, the proposed approach has identical noise suppression of the classical version; however, there is a clear reduction in the complexity from exponential function of image size \(O(2^{2n})\) to the second-order polynomial \(O(n^{2} + q)\).