改进的匹配追踪在方波信号滤波中的应用

Implication of improved matching pursuit in de-noising for square wave

为了克服常规滤波方法对方波信号滤波能力的不足,实现对方波信号的精确滤波,提出了一种改进的匹配追踪算法。针对方波信号特征,构建了与方波信号匹配而对噪声不敏感的方波原子;基于正交匹配追踪,并吸收子空间追踪的回溯思想,改进了最优原子选择方法;鉴于有用信号与噪声信号的能量差异,使用了一种自适应迭代停止标准,能准确找到有用信号和噪声的临界点,解决噪声能量未知的预估问题。对不同信噪比下的仿真方波信号进行滤波,经实测验证,所提方法在信噪比和均方误差方面都优于常规去噪算法,且保留了方波的特征,适用于方波信号的滤波。

To overcome the shortcomings of conventional filter methods for square wave signals, and realize precise de-noising for square wave signals, an improved matching pursuit algorithm was proposed. Firstly, the square atom, which matches with square wave signals and is insensitive to noises, was constructed specially based on the features of square wave signals. Secondly, an improved best atom selecting algorithm combined with the backtracking algorithm of subspace pursuit was applied based on orthogonal matching pursuit. In addition, in view of the different energy distributions between the true signal and noises, an adaptive iterative stop criterion was put forward, which can find precise critical point between the true signal and noises, and so the estimation problem of the unknown noise energy is solved. In the filtering of the simulated square wave signal with different signal to noise ratios, the method is superior in both of signal to noise ratio and mean square error to the conventional de-noising methods. Validated by measured square wave signals, the algorithm reserves more features of square waves compared with the conventional de-noising approaches, and it is appropriate for the de-noising of square wave signals.