Görsel uyarılmış potansiyellerin kalman süzgeci ile kestirimi
Estimation of visual evoked potantials by means of kalman filtering
- Tez No: 39124
- Danışmanlar: DOÇ.DR. MEHMET KORÜREK
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 80
Özet
ÖZET Fiziksel bir dış uyarımla EEG'de meydana gelen potansiyel değişimlerine uyarılmış potansiyeller denir. Bu tezde, görsel uyarılmış potansiyellerin kestirimi için bir yöntem incelenerek uygulanmıştır. Bu yöntemde yapılan ölçüm uyarılmış ve kendinden varolan iki bileşenin toplamı olarak düşünül muş t Ur. Her iki bileşenin de gözlenebilir özellikleri göz önüne alınarak bileşik bir durum uzayı modeli oluşturulmuş tur. Bu modelde kendinden varolan etkinlik öz bağlanımlı bir süreç olarak tanımlanmış ve karakteristikleri ölçülen etkinliğin uyarı öncesi kısmından kestirilmiş tir. Uyarılmış potansiyel doğrusal bir sistemin dürtü yanıtı olarak modellenmiştir. UP'nin karekteristikleri ortalama dalga şeklinden çıkarılmıştır. Parametrik sistem teorisi ile bütün modelin bir durum uzayı gösterimi elde edilmiştir. Modelin durum uzayı gösterimi esas alınarak, sistem durumunu gözlemek amacıyla her iki etkinlik içinde optimum kestirimlerde bulunan bir Kalman süzgeci tasarlanmıştır. Gerçeklenen yöntemin özellikleri benzeşim verilerine uygulanarak denenmiştir. Son olarak yöntem ölçülmüş gerçek verilere uygulanmıştır. Giriş ve çıkış işaret gürültü oranları hesaplanarak yapılan kestir imin hassasiyeti belirlenmiştir.
Özet (Çeviri)
SUMMARY ESTIMATION OF VISUAL EVOKED POTANTIALS BY MEANS OF KALMAN FILTERING The recording of the electrical activity of the brain is known as electroencephalogram . Brain potantials which are elicited external stimuli is called evoked potantials , EP's are responses in the EEG to specific activation of sensory pathways. Evoked brain potentials are measured using one or more scalp elctrodes and most generally referencing the measurements to a position such as linked ears. In this thesis, a system theoretic approach is described which is based on parametric models describing the data generating processes. The poststimulus EEG activity is assumed to be an additive superposition of an evoked and a spontaneous part. The characteristics of the spontaneous EEG are estimated from the activity measured immediately before each stimulus, while those of the EP are derived from the average waveform. A compound state space model trying to incorporate the observable properties of both parts is formulated on the basis of additivity of the two components. The spontaneous EEG is modelled as the output of a linear system driven by white noise. It is described as an autoregressive CAR) process. We thus write, e+s CD where e is the white input noise. For estimating the AR parameters and the variance of the input noise from measured data the Burg algorithm used. The fixed values in the range from 5 to 13 are proposed for the model order p. The EP is modeled by an impulse response of a parametrically described system. The system is characterized by the vector of parameters c s where, s, c is the vector of parameters, and s is the vector of past values of the output and the input signal. The conventional averaged data served as a template for the single EP's. M y t=d... d+N-1 MJ=i J Where y. 's are the measured single trials, and M is the number of stimulus repetitions. Therefore, an estimate of the vector parameters c is obtained by fitting the impulse response of the system to the average measured data, using y instead of unknown s(t). The least squres method was chosen for fitting the parameters. When the N values of the template y The estimated parameter vector c_can be determined with using standart numerical methods like cholesky decomposition. For the signals at hand, the model orders between S -11 were appropriate. In order to take into account of the variabilities of the EP under repeated stimulation, a stochastic amplification factor A and a stochastic latency shift L are introduced to form the entire EP model: s J J J According to the definition, the mean of the stochastic amplification factor A has to be 1. From the mean and variance of both stochastic elements, the mean and variance of the input signal to the determi nistic element are easily obtained for unit impulse input u ~2 var ] =P > A (6) Where P is the probablity of shift L=t, and S is the variance of the random amplification factor A. The described model assumes the single responses to be a scaled and shifted version of the template. Using additivity, a state-space represantation of the combined EEG-UP model can be set up with a compound state vector x comprising the two partial models. x=Fx+Bu y=Hx Where F is the system matrix, B is the input matrix, D is the noise input matrix, H is the output matrix, w is the - 2 output measurement noise with variance S. V X e F= 0. c d d 0.. m. O. n. 0...1 0 0. 0.... 0 o. 0.... o o. 0 0 0. o o....0 0...00. 0 a 0 0. 0 0 i 0 0 o. a 1 0 The input matrix B, the noise input matrix D the output matrix H: and is the input noise with variance given by , and w is the noise input to EEG model. The compo nents of the noise input vector w are independent and the cross-ponding covariance matrix is diagonal, aFT+DQDT covariance of the predicted state Oil) k x=x+k-Hx> estimated state =H>P co variance of estimated state measured up to then are exclusively due to spontaneous activity measured with the measurement- noise. Thus, t fee initial values are assigned to the estimated state x o and the corresponding cova- xCt t >: o ı o y. o y o P = o ı o 0..0 0...0 o o 0 0.. o o.. o o.. 0 0.. o o. o o. o o o s2 0 0...0 0..0.0.0.0 :s2 The entire procedure for the extraction of spontaneous and evoked activity from a given set of data can be summarized as folows: 1. Preprocessing: If allowed by present data, these should be bandpass-filtered and afterwards subsampled to the lowest possible sampling rate in order to reduce the computational burden of the following steps. 2. Ep parameters data modelling: The data are averaged and the of the EP model are fitted to the average method. The variance of the by least -squares model S is estimated using the presti mul us variance of the average. The presumed variabilities of amplitude and latency are converted to mean and variance of the input signal. 3. EEG modelling: From the measured single trial prestimulus interval the parameters and the variance of the EEG model are estimated by Burg algorithm. 4. Initialization: The estimated state vector and its covariance matrix are initilized for a presti mules time point. 5. Filtering: Using the described Kalman filter, a state vector, and thus evoked and spontaneous activity, is estimated for each subsequent time point. The properties of the proposed method are tested by application to stimulated data in which preset EP's are added to measured spontaneous EEG segments. Finally, the method is applied to real data.
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