Review: Prediction of Respiratory Motion - Prediction and Classification of Respiratory Motion - page 21

0
@

1
A

a 11 a 12 a 13 a 14

a 21 a 22 a 23 0

A ð t Þ¼

; ð 2 : 9 Þ

a 31 0 a 33 a 34

a 41 a 42 0 a 44

To predict motion with HMM, the future position of an observation is calcu-
lated using the velocity parameter (v i ) based on FSM,
x ð t Þ¼ x ð t 1 Þþ X
l

v l s ; ð 2 : 10 Þ

where variable s (=1/RT) consists of the sampling rate (R) and the estimated cycle
period (T), and l represents the dimension. Kalet et al. showed that the RMSEs of
ideal HMM and linear prediction are 1.88 and 2.27 mm with 200 ms latency. The
limitation of this model is that the implemented algorithm is based on stochastic
process so that the prediction results can be different even with the same data [ 73 ].
We summarized the prediction accuracy and a representative feature for each
method of the model-based approach, as shown in Table 2.2 .

2.3.2 Model-Free Prediction Algorithms

Model-free heuristic learning algorithms, exemplified by linear adaptive filters
and neural networks variables, can be used for the respiratory prediction for
compensating for the impaired breathing signal with a variety of breathing
patterns [ 57 , 74 , 79 , 93 ]. These heuristic learning algorithms can adjust their
coefficients/weights or configurations to reproduce newly arrived breathing sig-
nals without a priori models of signal history [ 93 ]. In this chapter, we will explain
two representative learning algorithms and adaptive systems for tumor prediction
including (1) adaptive filters [ 57 , 74 , 79 , 93 - 95 ], and (2) artificial neural network
[ 57 , 75 , 79 , 82 , 93 ].

2.3.2.1 Adaptive Filters

An adaptive filter is a self-adaptive system that can adjust its coefficient values
over time according to an optimization process incurred by an error signal, such as
least mean squares (LMS) and recursive least squares (RLS) algorithms [ 96 ]. The
adaptive filter depicted in Fig. 2.11 shows the basic adaptive filtering process for
prediction.
The predicted position x(t) can be expressed by a vector of previous respiratory
motion x(t - i) and a vector of filter coefficients w i (t), as follows: