为解决数学形态滤波器结构元素参数优化问题，提出了一种基于量子遗传算法的数学形态滤波器优化设计方法．根据数学形态结构元素参数特点初始化量子遗传种群，通过量子交叉、变异、基于膨胀系数的量子旋转门实现种群的演化进程，进而得到数学形态滤波器的最佳参数．结合仿真实验，研究了不同比例随机噪声、工频干扰噪声下的优化算法性能．仿真结果表明：优化后的数学形态滤波器性能得到较大改善，含随机噪声信号的信噪比由-0．98 dB提高到5．23 dB，含混合噪声信号的信噪比由-3．05 dB提高到0．41 dB，有效滤除了随机噪声、混入工频干扰的混合噪声．%To deal with the structuring element optimization of mathematical morphology filter,an optimization design method of mathematical morphology filter based on quantum genetic algorithm was proposed. The quantum genetic population was initialized according to the characteristic of mathematical morphology structuring element parameters. The population evolution was realized by quantum crossover,variation and quantum rotation gate based on expansion coefficient,thus obtaining the best parameters of the mathematical morphology filter. The performances of optimization algorithm under different proportions of random noise and power frequency interference noise were studied. The simulation results show that the performance of mathematical morphology filter is greatly improved after being optimized. The signal-to-noise ratio of the signal with random noise is improved from -0. 98 dB to 5. 23 dB,and that of the signal with mixed noise is improved from -3. 05 dB to 0. 41 dB. It means that the optimized mathematical morphology filter could remove both random noise and mixed noise with power frequency interference effectively.
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