基于噪声相关特性的数学形态学消噪原理研究

Research on the principle of mathematical morphology denoising based on noise correlation

结合电力信号采集中噪声的相关性理论和数学形态学基本原理,通过数值仿真详细研究了自相关噪声和随机白噪声干扰下,数学形态学滤波中关于结构元素如何选取的问题。分析指出,针对自相关噪声,结构元素的选择与噪声的周期性,最大峰值及采样率等因素密切相关。类似高频正弦噪声,通过选择合适尺度的正余弦形或三角形结构元素进行形态滤波均能取得良好的滤波效果。而对于随机白噪声而言,由于不具有自相关特性,因此并不存在类似相关噪声下的结构元素选取规律,多数情况需要通过预先的仿真或根据经验来合理选择结构元素。

Combined with the correlation theory of noise and the basic theory of mathematical morphology in power signal acquisition,in this paper,the selection rules of structural elements in mathematical morphology filtering in the case of correlated noises and random white noise are studied by numerical simulation in detail. It is pointed out that the choice of the structural elements is closely related to the periodicity of the noise,the maximum peak value and the sampling rate. Similar to the high frequency sinusoidal noise,the good filtering effect can be achieved through the choice of the appropriate size of the sine and cosine shaped or triangular elements of the morphological filter. There are no similar selection rules of structural elements under the random white noise due to the absence of autocorrelation. Therefore,there is no similar structural elements selection law under the noises correlation,which needs to be reasonably selected according to the experience or pre-simulation in most of the cases.