基于Mumford-Shah泛函的数字信号去噪算法

New digital signal denoising algorithm based on Mumford-Shah functional

针对数字信号处理中的去噪技术问题,利用Mumford Shah泛函模型的特点进行去噪研究.对应用于图像处理中的二维Mumford Shah泛函进行简化和降维处理,建立适合于数字信号去噪处理的一维Mumford Shah泛函,利用能量最小化原理的变分方法导出一个新的去噪处理模型,并提出两种不同的计算算法:区域合并算法和点集扩张算法.在点集扩张算法中利用了统计学中常用的逐步分析方法,保证了处理结果的整体最优性.实验结果表明,两种算法均能有效地消除信号中的噪声,同时精确地提取出信号中的特征点.与Pollak Willsky算法相比较,新的去噪处理模型能更好的保持信号中的原始特征信息.

The problem of denoising technique in digital signal processing was analyzed by using the characteristics of the Mumford-Shah functional model. Two-dimensional Mumford-Shah function was simplified and reduced to one-dimensional case. A new signal denoising model was presented which based on the one-dimensional version and the variational theory. Two numerical algorithms for the new model were described: region merging algorithm and points-set growing algorithm. The latter algorithm has global optimization by applying the step-by-step analytical method of statistics. Numerical results show that the algorithms can restore noised signal effectively, and detect the jumping points simultaneously. Compared to the Pollak-Willsky algorithm, the presented algorithms can preserve the original signal structures more precisely.