Review: Prediction of Respiratory Motion - Prediction and Classification of Respiratory Motion - page 22

Desired signal d ( t )

Predicted position

x ˆ t )

+

Input signal
x ( t )

Adaptive transfer
Function with w i ( t )

Delay

Σ

−

Error signal e ( t )

Fig. 2.11 Basic adaptive filtering process for prediction. The predicted position is calculated
using the combination of previous respiratory motion x(t - i) multiplied by its coefficient values
w i (t). Here the coefficient values are time-variable according to an optimization process incurred
by an error signal e(t)

x ð t Þ¼ X

n

w i ð t Þ x ð t i Þ; ð 2 : 11 Þ

i ¼ 1

where filter coefficients change over time. Adaptive filters were widely used to
predict the tumor motion [ 57 , 74 , 79 , 93 , 95 ]. Vedam et al. proved that adaptive
filter models have the prediction accuracy with less than 2 mm and outperform
sinusoidal models [ 74 ]. Although the adaptive filter has a limitation with 1D
prediction, it is extended into multi-dimensional adaptive filer [ 56 ]. Adaptive
models can also be adjusted to update the weights of neural networks to improve
the prediction accuracy [ 57 , 79 , 94 ].

2.3.2.2 Artificial Neural Network

An artificial neural network (ANN), commonly called neural network (NN), is a
mathematical

or computational function technique that is inspired by the

Hidden ( y j )

w ij

1 1

w jk

Input ( x i ) 1

n i j Output ( z k )

k

Bias B n h

Fig. 2.12 An artificial neural network with bias input and one hidden layer. The network
consists of input, hidden, and output layers interconnected with directed weights (w), where we
denote w ij as the input-to-hidden layer weights at the hidden neuron j and w jk as the hidden-to-
output layer weights at the output neuron k