Adaptive Signal Decomposition And Its Application On Nonparameter Signal Denoising

Signal decomposition is one of the most important analysis methods in signal processing area.Its goal is to decompose the sophisticated signal into several basic components for extracting more useful information.However,for the signals obtained in the complex environment,the performance is usually not satisfactory by using the conventional signal decomposition methods like Fourier decomposition and wavelet analysis.One of the most important reasons is that these methods must predefine the basis functions.Therefore,they lack of adaptiveness.In other words,a predefined basis function works well toward a signal while it is not effective for some other signals.Adaptive signal decomposition is more suitable for the analysis of the sophisticated and fickle signals because it does not need to predefine basis functions.Recently,adaptive signal decomposition has attracted widespread attention of researchers and become a hot topic in signal processing and signal analysis area.This thesis focuses on the research on adaptive signal decomposition especially the empirical mode decomposition(EMD)and the singular spectrum analysis(SSA).Further,the thesis explores the nonlinear and adaptive hierarchical multiresolution analysis based on EMD.Also,the thesis applied EMD and SSA to nonparameter signal denoising.The research includes the following aspects:1.The nonlinear and adaptive hierarchical multiresolution analysis method based on EMD is proposed.The current intrinsic mode function(IMF)obtained by EMD cannot be directly decomposed into several IMFs in the next level since the current IMF satisfies the stop criterions of EMD.Therefore,EMD cannot provide a pyramid like framework for representing signals like wavelet multiresolution analysis.In order to achieve the next level decomposition of IMF,an algorithm is proposed in this thesis.An IMF is expressed in the frequency domain by applying discrete Fourier transform(DFT)to it.Next,zeros are inserted to the DFT sequence.Then,inverse discrete Fourier transform(IDFT)is applied to the zero padded DFT sequence and a new signal expressed in the time domain is obtained.The next level IMFs can be obtained by applying the EMD algorithm to this signal.However,the lengths of these next level IMFs are increased.To reduce these lengths and reconstruct the original IMF,DFT is first applied to each next level IMF.Second,the DFT coefficients of each next level IMF at the positions where the zeros are inserted before are removed.Finally,by applying IDFT to the shorten DFT sequence of each next level IMF,the final set of next level IMFs are obtained.Compared to the conventional wavelet multiresolution analysis,the proposed method can not only achieve the hierarchical multiresolution analysis but also succeed the advantages of nonlinearity and adaptiveness of EMD.2.Based on the fact that the sums of logarithms of the energies and mean periods of the IMFs of the white Gaussian noise are constants,the analytical form of the constants is proposed in this thesis.By exploiting the constants,a nonparameter denoising method is proposed.Since the increasingly larger fluctuations occur for the modes as the indices increase,the training process is conducted only using some low order and reliable IMFs.By using extensive white Gaussian noise samples,the maximum and the minimum relative percentage errors between the modle based constant and the real constants are trained.When conducting the nonparameter denoising,the upper bound and the lower bound which indicate the noise dominated IMFs are generated by using the maximum and the minimum relative percentage errors and the model based constant.Then,the first point which is out of the bounds is record.Finally,the IMFs whose indices are equal to or larger than the point are employed to reconstruct the denoised signal.Since the improper parameter will lead to bad denoising performance,the proposed method can avoids the problem because of its nonparameter characteristic.Experimental results show that the proposed method outperforms some existing EMD based nonparameter denoising methods.3.The reduction of quantization noise based on SSA is proposed in this these.The reconstructed signal is modeled as the weighted sum of the SSA components.In order to estimate the weights,each quantization level is considered as a class.If the signal value is close to a quantization level,then the probability of having the signal value belonging to this class is relatively high.On the other hand,if the signal value is far away from the quantization level,then the probability is low.The signal values are associated with the probabilities of the classes via the sigmoid functions defined based on the distances between the signal values and the quantization levels.Therefore,the reconstruction problem can be considered as a classification problem.The optimal estimate of a given signal in the minimum cross entropy sense can be provided.Because the last several eigenvalues may be nearly equal to zero for some signals in the SSA procedures particularly when the windows length is large,the corresponding vectors of the SSA components will be close to the zero vectors.Therefore,the conventional mean squares error criterion suffers from the ill posed issue.Since the signal values are restricted to the range between 0 and 1 due to the probability constraint,the minimum cross entropy criterion will work properly.Also,SSA is a nonparametric spectral estimation method.Therefore,the proposed method enjoys the advantage of adaptiveness.Experimental results show that our proposed method can reduce the quantization error and reconstruct the original signal more accurately compared to lowpass filter and Wiener filter.In summary,compared to conventional signal decomposition methods,the adaptive signal decomposition has large potential to obtain more useful information from the sophisticate signals.The thesis focuses on the research on adaptive signal decomposition especially EMD and SSA.In this thesis,the nonlinear and adaptive hierarchical multiresolution analysis based on EMD is proposed while the study on the nonparameter reduction of white Gaussian noise and quantization noise based on EMD and SSA is also conducted.These researches are significant no matter in theory or in practical engineering application.