The Null Space Pursuit Algorithm Based On Differential Operator And Its Application In Physiological Signal Processing

With the rapid development of computer and electronic information technology,digital signal processing technology theory,algorithms and means of implementation attracts more and more people's attention.In this case,the representation and decomposition of the signal is the prefer direction we want to study.Many scholars in this field put forward a lot of ways to break down a signal into the form of several signals.To some extent,signal decomposition is signal model representation.In this paper,the Null Space Pursuit algorithm based on differential operator is a good method on signal decomposition.Null Space Pursuit(NSP)algorithm based on differential operator is an important method in signal denoising and signal decomposition.The algorithm is a new adaptive signal decomposition algorithm proposed by Professor Silong Peng and Professor Wenliang Huang in 2008.It is different from other decomposition methods,which define a differential operator that makes the decomposed signal in the null space of the differential operator we define.Since the different signals will belong to the null space of different order differential operators,in order to make the signal decomposition range is more extensive,Dr.Xiyuan Hu extended null space pursuit algorithm in 2011.After that,many researchers have proposed different types of differential operators,has been improved the range of decomposable signals.In this paper,we apply even order differential operator to the null space pursuit algorithm.We determined the order of the differential operator according to the characteristics of the input signal.Then,by solving the optimization problem,determine the form of the differential operator by estimate the value of the parameters.Finally,we prove the feasibility of the algorithm.In the third part of this paper,we use the null space pursuit algorithm to denoise the actual physiological signal EEG.Then,we analyze experts' classification results,and give sleeping period classification method from the frequency and the numerical distribution characteristics of the signal.After that we find a new classification standard that applied to any EEG data.The results show that the degree of coincidence of our classification results and expert classification results is about eighty percent,Which proves our classification standard is feasible.