The Study Of The Noise Suppression Effect Of The CLAD Deconvolution Method

Auditory evoked potentials (AEPs) is a series of electrical signals with a certain intensity and a constant latency originated from cochlear hair cells and auditory nervous system in response to a external and specific acoustic stimulation. it reflects physiological characteristics and health status of the human brain and auditory neural pathways. According to different types of stimulation rate, it can be can be divided into conventional auditory evoked potentials and high stimulus rate Auditory evoked potential. Conventional auditory evoked potential has been widely used in clinical practice, while high stimulus rate Auditory evoked potential is still in the stage of scientific research instead of clinical application. According to the different latency, auditory evoked potentials can be divided into the following sections:auditory brainstem response (ABR), Middle latency responses (MLR) and late latency response (LLR), that reflect physiological characteristics of different parts of the auditory system. Currently, AEP has been successfully used in evaluation of infant hearing and diagnosis of auditory nerve lesions, etc. Clinically, AEP’s records are carried out in a low stimulation rate and equal stimulus onset asynchrony stimulation method, applying ensemble averaging technique to improve the signal to noise ratio. However, with stimulus rate improving, when stimulus onset asynchrony (SOA) between two adjacent stimulus is less than the duration of the single high-order AEP, it appears that adjacent two or several high-order AEPs produce overlap phenomenon. The overlapped AEP is defined as high stimulus rate AEP(HSR-AEP). High frequency sound stimulus Adds to the auditory nerve load, which makes auditory neural pathways and brain lesions sensitive and contributes to the evaluation of anesthetic depth monitoring and sleep state. Meanwhile, under the premise of the same number stimulus, high stimulus rate AEP can shorten the time of recording, and it is of great significance for some children and non-cooperative subjects in clinical detection. Therefore, the study of high stimulus rate AEP is very important in theoretical research and clinical applications.However, for the study of high stimulus rate AEP, we must solve the crucial problem of transient AEP reconstruction from the steady-state response, although traditional ensemble averaging methods can improve the SNR of steady-state AEP, but it can’t solve the overlapping problem between high -order AEPs and stimulus sequences. The overlapping phenomenon between high-order AEPs and stimulus sequences corresponds to convolution model. Hence, reconstructing transient AEP from the steady-state response is essentially a process of inverse convolution. Based on this model, if jitter random numbers within a certain range instead of the constant stimulus onset asynchrony(SOA), transient evoked potentials can be extracted by deconvolution technique. At present, there is four kind of relatively sophisticated deconvolution techniques, which mainly includes the followings:Maximum length sequence technique (MLS); Continuous loop averaging deconvolution technique(CLAD); Quasi-periodic sequence deconvolution technique(QSD); Multi-rate steady-state averaging deconvolution technique (MSAD).MLS is a kind of pseudo random binary sequence in accordance with strict mathematical theory, which is calculated and designed by Davies in 1996. it restores the transient AEP on the basis of the sequence’s autocorrelation by deconvolution. In General, AEP signals which is got by MLS have a low signal to noise ratio(SNR), stimulate the number needs to be increased in order to gain the same SNR as a general method. Meanwhile, the large differences from AEPs got by MLS with multiple change SOA damages the linear convolution models. Continuous loop averaging deconvolution technique (CLAD) was first proposed by Delgado and Ozdamar in 2004, which mainly generates invertible matrices by stimulus sequences, then reconstructs AEP by inverse filter in the frequency domain. In CALD technique, the non-equispaced sequence with random jitter on a smaller scale is used to make generated matrix invertible by stimulus sequence, and prevent the emergence of the singular values. The frequency domain characteristic of a Stimulus sequence is the key to determine the effect of transient AEP reconstruction. Quasi-periodic sequence deconvolution technique(QSD) is similar to Continuous loop averaging deconvolution technique(CLAD), which is proposed by Jewett, in accordance with certain constraints. Because of strong inhibitions against noise and it improves the quality of AEP reconstruction. The core idea of MSAD is that convolutional model between traditional HO-AEPs and stimulus sequences is again expressed by linear transformation. Deconvolution is implemented by inverse matrix,that is used is to restore the original high-order AEP. the implementation of this technology requires to choose reasonable regularization parameters in order to void the distortion of transient AEP waveform. This paper focused on the relationship between the characteristics of stimulus sequences and noise suppression effect, Furthermore, to explore the relationship between gain factor Cdec and the quality of the AEP reconstruction.Continuous loop averaging deconvolution technique(CLAD), which bases on the mathematical theory:cyclic convolution model and the Fourier transform, tansforms convolution model in time domain to the multiplication model in frequency domain. thus, it achieves the complex convolution into the simple multiplication, After the spectrum of AEP signal divides by the spectrum of stimulus sequence, and through the inverse Fourier transform transient AEP that we need can be extracted. But in the real problem, the steady-state AEP that we recorded is involved in background noise with EEG Through the traditional ensemble averaging method can eliminate white noise with random uniform distribution, but not eliminate EEG background noise with regular distribution. These residual noise in the deconvolution process is likely to excessively amplified by the inverse filter, which leads to the distortion of HO-AEP signal recovery. Therefore, in CLAD deconvolution technique, it is vital important to ensure the noise suppression capability of stimulus sequence. For a reasonable solution to this critical issue, we can consider two points:Firstly, choose excellent stimulation sequences according to characteristics of stimulus sequence, which requires a reasonable constraint for the choice of stimulation sequences. Secondly, a reasonable standard parameter for evaluating the performance of stimulus sequence needs to be proposed. The second condition is to ensure the first one. Currently, Jewett proposes that spectral amplitude of the inverse filter should be less than the threshold value 1 in our interest passband range, in order to ensure that the noise in our interested frequency band is not amplified. based on the assumption of uniform distribution of noise, Ozdamar, combined with the Paresval theorem, who proposes a standard parameter for evaluating the performance of stimulus sequence (known as Cdec).The former can be used as a condition to restrain stimulus sequences, but this constraint for each frequency makes jitter index of a sequence lower; the latter can be used as parameters, but whose hypothesis is not consistent with the distribution of actual EEG noise. In our study, these results can be verified in our experiments.As mentioned above, CLAD technology does not eliminate the effects of additive noise on the signal quality. Therefore, in the process of deconvolution, analysis of signal to noise ratio is a very meaningful work. Two factors that have an impact on the quality of AEP signal reconstruction:firstly, the spectrum distribution characteristics of EEG(Electroencephalogram, EEG) noise. secondly, inverse filter frequency response function. Based on the assumption of uniform distribution of noise, the amplitude of inverse filter is calculated in the ensemble averaging method, according to these, Ozdamar terms gain factor Cdec as a parameter for evaluating the performance of stimulus sequence in the frequency range of interest. Gain factor Cdec provides a standard to generate an select stimulus sequence. However, Freeman’s research shows that AEP’s background noise, which mainly refers to EEG, is not white noise. its distribution in the frequency-domain shows inverse proportion and energy is concentrated in the low frequency range. Because of characteristics of non-uniform distribution, Gain actor Cdec can’t reflect the performance of stimulus sequence steadily. At present, the characteristic of noise distribution and inverse filter frequency response functions is how to affect the SNR of the reconstruction process and so on. with regard to this issue, few studies is carried out. This paper discusses noise amplification mechanism in the process of AEP signal reconstruction on basis of CLAD deconvolution technique. by real experiments, background noises from AEP that we recorded are analyzed and the relationship between the quality of HO-AEP reconstruction and stimulus sequence is explored, which provides a theoretical basis for further improving the assessment of the noise suppression capability of stimulus sequence.