量子线性卷积及其在图像处理中的应用  

Quantum Linear Convolution and Its Application in Image Processing

作　　者：刘兴奥 周日贵 郭文宇 LIU Xing-Ao;ZHOU Ri-Gui;GUO Wen-Yu(College of Information Engineering,Shanghai Maritime University,Shanghai 201306;Research Center of Intelligent Information Processing and Quantum Intelligent Computing,Shanghai 201306)

机构地区：[1]上海海事大学信息工程学院,上海201306 [2]上海海事大学智能信息处理与量子智能计算研究中心,上海201306

出　　处：《自动化学报》2022年第6期1504-1519,共16页Acta Automatica Sinica

基　　金：上海市科技项目(20040501500)资助。

摘　　要：线性卷积在图像处理中发挥着重要作用,但是在处理海量高分辨率图像时,求解线性卷积会消耗许多计算资源.为此,本文就量子线性卷积及其在图像处理问题中的应用开展相关研究,首先提出单通道,单位步长,零补充情况下的量子一维和二维线性卷积,然后实现多通道,非单位步长,非零补充的情况,最后将量子二维线性卷积应用于量子图像平滑,量子图像锐化和量子图像边缘检测.通过理论分析证明了量子线性卷积的空间复杂度O(logM)和时间复杂度O(log^(2)M)较经典线性卷积有指数级下降,且基于Qiskit的仿真实验成功验证了量子线性卷积和量子图像处理算法的正确性和可行性.Linear convolution plays an important role in image processing,but when processing massive high-resolution images,solving linear convolution will consume a lot of computing resources.To this end,this paper conducts related research on quantum linear convolution and its application in image processing problems.We first propose the quantum one-dimensional and two-dimensional linear convolution in the case of single channel,unit stride and zero padding,and then implement the case of multi channel,non-unit stride and non-zero padding.Finally,we apply the quantum two-dimensional linear convolution to quantum image smoothing,quantum image sharpening and quantum image edge detection.Through theoretical analysis,it is proved that the space complexity O(logM) and time complexity O(log^(2)M) of quantum linear convolution decrease exponentially compared with classical linear convolution,and the simulation experiment based on Qiskit successfully verifies the correctness and feasibility of the quantum linear convolution and quantum image processing algorithms.

关 键 词：量子线性卷积 量子图像平滑 量子图像锐化 量子图像边缘检测 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O413[自动化与计算机技术—计算机科学与技术]