Wavelet Denoising Based On Improved Threshold Function And Its Optimization Research

In the systemof computer control,owing to the influence of environment or the nature of the work,the transmission,detection and collection of the signal will be subject to pollution of varying degrees of random noise,accordingly,the implementation of signal de-noising is necessary.How to filter out the noise in the real signal and get effective information is also one of the current research hotspots.Especially for the mixed signal of high frequency and strong noise?weak signals or non-stationary random signals,the traditional Fourier transform which could handle stationary signal can not be analyzed locally.Because the wavelet transform has a time-frequency local analysis function,the use of wavelet transform de-noising results are relatively good,and its application is also very extensive.From the few methods of wavelet de-noising,the wavelet threshold shrinkage de-noising method can be close to the optimal in the sense of minimum mean square error,and it has good visual effect,and it is widely used and deeply studied.In the method of wavelet threshold de-noising,the wavelet basis,the numbers of decomposed layer,the threshold value and the threshold functions are the important factors of wavelet threshold de-noising.For a variety of noisy signals,not the same wavelet basis has different characteristics,and it can be very sure that:no wavelet basis function can achieve the best effect for all types of signal by de-noising.At the same time,for the number of layers of the decomposition,it can be very certain that:with different signals and not the same signal to noise ratio,there is a best number of decomposition layers about de-noising effect or close to the best.In this paper,an algorithm is proposed for the determination of the wavelet basis and the number of decomposed layers.It can analyze the signal to be processed.With the signal-to-noise ratio as an index,the algorithm calculates the improvement of signal-to-noise ratio by signal processing with using different wavelet basis function or decomposed layer numbers.And it obtains the relationship to determine the most appropriate wavelet basis function and the number of decomposed layers.The selection of the threshold function directly affects the signal reconstruction accuracy.For the previous hard and soft threshold function,there are some shortcomings:the curve of hard threshold function is not continuous at the threshold,and the existence of the phenomenon of discontinuity,after de-noising,a breakpoint signs will make the reconstruction signal is more prone to additional oscillation and the resulting in "pseudo Gibbs" phenomenon.The wavelet coefficients which are greater than the threshold function are usually mixed with the noise signal disturbance,affecting the quality of the last reconstructed signal;soft threshold function also has its own defect:In the threshold processing,when the absolute value of the wavelet coefficients is greater than or equal to this threshold value,the wavelet coefficients are subtracted from the thresholds,which will make the constant deviation between the wavelet estimation coefficient and the original signal wavelet coefficients,and it will directly affect the effect of the last reconstruction signal.In view of the shortcomings of traditional threshold function,many scholars propose many improved threshold function algorithms between soft and hard thresholds.However,these threshold functions are not derivable in the whole wavelet domain,and there is a phenomenon that these are not transition smoothly at the critical threshold.Therefore,this paper proposes a threshold function with parameters,which has a higher order.It can be between hard and soft threshold function through the parameters adjusted flexibility and possessing the advantages of both hard and soft threshold function.What's more,it could retain the high frequency part of some useful signal by threshold processing and effectively suppress the stifle of detail coefficients and the phenomenon of signal oscillation.Simulation results showed that new threshold function increases the signal-to-noise ratio of signal,reduces the mean square error and obtains a relatively good de-noising effect.In the process of de-noising with using the parameter threshold function,the parameters of the threshold function can be flexibly adjusted for the specific noisy signal to meet the de-noising requirements of different signal processing.However,in practical applications,the noisy condition of the signal to be processed is unpredictable or unknowable.For de-noising of this random variation of the noisy signal,the parameters of the threshold function should not and could not be a fixed value.Therefore,for the threshold processing of random noisy signals,the appropriate optimization algorithm is selected to optimize the parameters of the threshold function in order to be able to adapt to the signal change,which is the key to de-noising to practical.The threshold function has two parameters,and there are fewer parameters when the function is optimized,at the same time,it is necessary that the optimization target is completed in a short time.Therefore,the optimization algorithm which has relatively high convergence speed is needed.Compared with simulated annealing algorithm,genetic algorithm,neural network algorithm and ant colony algorithm,the particle swarm optimization algorithm which has high convergence speed,high precision and easy implementation and has not too much parameter adjustment was selected.The particle swarm optimization algorithm was used to automatically optimize the threshold function parameters for the noise condition of the signal,and the automatic optimization of the de-noising process was realized.The simulation results of benchmark signals showed that the proposed algorithm can obtain smaller Mean Square Error and higher signal-to-noise ratio,and the effect of de-noising is achieved.