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Quantum image median filtering in the spatial domain

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Abstract

Spatial filtering is one principal tool used in image processing for a broad spectrum of applications. Median filtering has become a prominent representation of spatial filtering because its performance in noise reduction is excellent. Although filtering of quantum images in the frequency domain has been described in the literature, and there is a one-to-one correspondence between linear spatial filters and filters in the frequency domain, median filtering is a nonlinear process that cannot be achieved in the frequency domain. We therefore investigated the spatial filtering of quantum image, focusing on the design method of the quantum median filter and applications in image de-noising. To this end, first, we presented the quantum circuits for three basic modules (i.e., Cycle Shift, Comparator, and Swap), and then, we design two composite modules (i.e., Sort and Median Calculation). We next constructed a complete quantum circuit that implements the median filtering task and present the results of several simulation experiments on some grayscale images with different noise patterns. Although experimental results show that the proposed scheme has almost the same noise suppression capacity as its classical counterpart, the complexity analysis shows that the proposed scheme can reduce the computational complexity of the classical median filter from the exponential function of image size n to the second-order polynomial function of image size n, so that the classical method can be speeded up.

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(figure adapted from [31])

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Acknowledgements

The authors appreciate the kind comments and constructive suggestions of three anonymous reviewers. This work was supported by the Natural Science Foundation of Heilongjiang Province of China (Grant No. F2015021). We thank Richard Haase, Ph.D, from Liwen Bianji, Edanz Group China (www.liwenbianji.cn/ac), for editing the English text of a draft of this manuscript.

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  1. School of Computer and Information Technology, Northeast Petroleum University, Daqing, 163318, China

    Panchi Li, Xiande Liu & Hong Xiao

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  1. Panchi Li
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  2. Xiande Liu
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Correspondence to Panchi Li.

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Li, P., Liu, X. & Xiao, H. Quantum image median filtering in the spatial domain. Quantum Inf Process 17, 49 (2018). https://doi.org/10.1007/s11128-018-1826-9

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