Quantum image K-nearest neighbor mean filtering

Quantum image filtering is an extension of classical image filtering algorithms, which mainly studies image filtering models based on quantum characteristics. The existing quantum image filtering focuses on noise detection and noise suppression, ignoring the effect of filtering on image boundaries. In this paper, a new quantum image filtering algorithm is proposed to realize the K-nearest neighbor mean filtering task, which can achieve the purpose of boundary preservation while suppressing noise. The main work includes: a new quantum compute module for calculating the absolute value of the difference between two non-negative integers is proposed, thus constructing the quantum circuit of the distance calculation module for calculating the grayscale distance between the neighborhood pixels and the center pixel; the existing quantum sorting module is improved to sort the neighborhood pixels with the distance as the sorting condition, and thus the quantum circuit of the K-nearest neighbor extraction module is constructed; the quantum circuit of the K-nearest neighbor mean calculation module is designed to calculate the gray mean of the selected neighbor pixels; finally, a complete quantum circuit of the proposed quantum image filtering algorithm is constructed, and carried out the image de-noising simulation experiment. The relevant experimental indicators show that the quantum image K-nearest neighbor mean filtering algorithm has the same effect on image noise suppression as the classical K-nearest neighbor mean filtering algorithm, but the time complexity of this method is reduced from $O\left(2^{2 n}\right)$ of the classical algorithm to $O\left(n^{2}+q^{2}\right)$.