Neural network based adaptive time frequency analysis of EGG signals

Abstract

AIM: This abstract introduces our study work on Neural Network based Adaptive Time frequency Analysis of EGG signals, which aims at adaptively extracting time frequency (TF) information of EGG signals by parameters learning algorithm based on Neural network and providing better TF resolution without any cross term interference.

METHODS: Given an EGG signal Egg (t) and a base function g(t)⊂LR² which satisfies ∥g(t)∥ = 1, Egg (t) can be estimated by the following relation,

Where IP (k) = {s (k), u (k), ξ (k), theta; (k) |k = 0, 1, ……K|}⊂LR⁺×R³ is the index parameter set which corresponds to scaling, shifting, center frequency and initial phase. D = g—ip (k), With ∥g—ip (k)∥ = 1, forms the dictionary of time frequency atoms, which is a very redundant set of function in L² (R) that includes window Fourier frames and wavelet frames. W—k is the weight parameter set. Given the size of the index set and the weight set, K, and the approximation error, ε, we can adjust these two sets by neural network based learning algorithm so that ‖Egg (t) - Egg (t)‖ < ε.

Math 1

Defining the least mean square (LMS) energy as

Math 2

one can learn the parameter sets by gradient algorithm, for example,

Wⁱ⁺¹—k = Wⁱ—k-α[(∂E)/(∂—k)], Sⁱ⁺¹—k = Sⁱ—k—β[(∂E)/(∂—k)]. Where subscript i is the iteration time and α, β are the learning vectors. As soon as the desired estimation estimation of Egg (t), Egg(t), is obtained, the next work is to computer the TF energy distribution. Performing Wigner distribution on Egg (t) in terms of that

Math 3

we can define a new TF energy distribution of Egg (t) by removing the crossterms of (2) as

Math 4

RESULTS: The simulations are performed by taking morlet wavelet base on four typical EGG data, representing normal, Tachygastria, Bradygastria and Arrhythmia respectively, which are provided by the Baptist medical center in United States. The two of the gray images of the TF energy distribution of the four sets of data are shown as follows (Figure 1).

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