Improved Quantum Image Filtering in the Spatial Domain

We investigate the quantum image filtering in spatial domain proposed by Yuan et al. (Int. J. Theor. Phys. 56(8), 2495-2511, 2017). Although the complexity of this algorithm is much better than the classical exhaustive algorithm, there may be a defect in it: the quantum multiplication was replaced by quantum addition. There are two shortcomings: 1) We should know exactly the value of the filter coefficients before each filtering behavior. 2) This method is only suitable for integer filter coefficients but not for decimal filter coefficients. In this paper, an improved version is proposed which takes full advantage of the quantum multiplication and can overcome these two shortcomings. The theoretical analysis indicates that the time complexity is the same as the previous algorithm. So this algorithm is also efficient.