Fast Extraction Algorithms For Evoked Potentials With Single Channel Measurements

Evoked potentials (EPs), which reflect the electrical activity of the corresponding sensory nerve pathways and cortical regions signal, can provide many important informations for the theoretical neuroscience researches and clinical applications. So in-depth analysis and study EPs are significant for not only the study of brain activity patterns and information processing mechanism, but also the disease diagnosis of possible brain injury and the intraoperative monitoring in surgeries. EP signals are usually deeply buried in the spontaneous electroencephalogram (EEG) signals. Therefore, how to extract EPs efficiently from strong EEG background noises is one of the most important issues in biomedical signal processing field. Coherent averaging (CA), which is still the most widely used method at present, has the drawbacks such as the loss of details of EPs and the large measurement errors due to the fatigue of central nervous system. So the studies of the fast extraction algorithms for EPs become a research hotspot and difficulty in recent years. Compared with the CA method, the fast extraction may be referred to as few-trial extraction, single-trial extraction or dynamic estimation.In this dissertation, we mainly studied the fast extraction algorithms for EPs with single channel measurements. The main researches and contributions are listed as follows:(1) Studied the few-trial extraction for EPs with single channel measurements based on sparse representation model, we respectively presented the mixed-trained-dictionary-based and the joint-sparse-representation-based methods. To overcome the drawback of error decompositions due to employ the common overcomplete dictionaries in existing method, we firstly proposed the mixed-trained-dictionary-based sparse representation (MTSR) method respectively according to the characteristics of EP and EEG signals. By training the adapted overcomplete dictionaries respectively for EP and EEG signals according to the template signal which is the average of few-trial observations, MTSR can effectively reduce the error decomposition problem. Secondly, according to the quasi-periodic characteristic of EPs, we proposed the joint-sparse-representation-based (JSR) method by employing few-trial adjacent observations and it can more effectively extract EPs at the relative lower signal-to-noise ratio (SNR) conditions.(2) Studied the single-trial extraction for EPs with single channel measurements based on the autocorrelation function of the underlying source signal, we proposed two kinds of waveform estimation methods based on the constraint by the autocorrelation function of the underlying source signal. We firstly proposed the autocorrelation constraint waveform estimation (ACWE) method according to the information obtained from the autocorrelation function of source signal. By constructing nonlinear equations and solving it with the large-scale equations numerical method, ACWE can change the directly estimation of source signal problem into an easier one, in which estimates the initial value and the autocorrelation function, respectively. ACWE has to spend much time to solve the nonlinear equations if the estimation accuracy of the autocorrelation function of the source signal is relatively lower. To overcome this drawback, we next proposed the autocorrelation optimization waveform estimation (AOWE) method. It can well balance between the estimation accuracy and computation speed and more suitable for applications requiring high computing efficiency. These two methods are used to the single-trial extraction for EPs with single channel measurements, and have achieved good estimation results.(3) Studied the adaptive estimation for EPs with impulsive noises with single channel measurements, we proposed three kinds of robust adaptive methods based on the radial basis function neural network model for EPs with single channel measurements. When the background noises of EPs present non-Gaussian impulsive characteristic, it is more suitable to be described by the α-stable distributions. To overcome the drawback of the least mean p-norm based method, which cannot work well when the a value dynamically changes, we firstly proposed the robust adaptive method based on the least mean absolute deviation (LMAD) criterion, and it can work well with a dynamically changing a value. Then to overcome the drawback of LMAD-based method, which cannot balance between the estimation accuracy and convergence speed due to the complete loss of amplitude of the error signal, we proposed the robust adaptive method based on the nonlinear Sigmoid transform (NLST) to estimate EPs with impulsive noises with single channel measurements. It can work well when the a value dynamically changes, and have better estimation accuracy and convergence speed due to effectively preserve the amplitude of the error signal. Finally we proposed the robust adaptive method based on the maximum correntropy criterion (MCC) to estimate EPs with impulsive noises with single channel measurements. By properly selecting the kernel width of the correntropy function, it can work well under the dynamically changing a conditions. All these three robust algorithms are employed to adaptively estimate EPs with impulsive noises with single channel measurements, and have achieved good estimation results.