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本文在对多尺度滤波和子波域滤波综述的基础上，用奇异性和自相似性理论对信号与噪声的不同性质进行了分析，揭示了信号与噪声的多尺度数学机理，并对基于此机理的Ｍａｌａｔ去噪声算法和子波域波波（ＷＴＤＦ）算法进行了研究，首次给出了ＷＴＤＦ的阈值选取方法和理论证明，完善和推广了ＷＴＤＦ，通过仿真计算表明，具有理论阈值的ＷＴＤＦ较之传统的试凑阈值ＷＴＤＦ性能有明显的改善。
Based on the review of multiscale filtering and wavelet domain filtering, this paper analyzes the different properties of signal and noise using singularity and self-similarity theory, and reveals the multi-scale mathematical mechanism of signal and noise. Based on this mechanism The algorithm of Malat de-noising and wavelet domain wave (WTDF) is studied. The method of WTDF threshold selection and theoretical proof are given for the first time. The WTDF is improved and generalized. The simulation results show that the WTDF with theoretical threshold is better than WTDF. The trial and error threshold WTDF performance has significantly improved.