DocumentCode :
744800
Title :
Neural filtering of colored noise based on Kalman filter structure
Author :
Xiong, Shen-Shu ; Zhou, Zhao-Ying
Author_Institution :
Dept. of Precision Instrum., Tsinghua Univ., Beijing, China
Volume :
52
Issue :
3
fYear :
2003
fDate :
6/1/2003 12:00:00 AM
Firstpage :
742
Lastpage :
747
Abstract :
In this paper, adaptive filtering approaches of colored noise based on the Kalman filter structure using neural networks are proposed, which need not extend the dimensions of the filter. The colored measurement noise is first modeled from a Gaussian white noise through a shaping filter. The Kalman filtering model of colored noise is then built by adopting an equivalent observation equation, which can avoid the dimension extension and complicated computations. An observation correlation-based algorithm is suggested to estimate the variance of the measurement noise by use of a single layer neural network. The Kalman gain can be obtained when a perfect knowledge of the plant model and noise variances is given. However, in some cases, the difficulties of the correlative method and the Kalman filter equations are the amount of computations and memory requirements. A neural estimator based on the Kalman filter structure is also analyzed as an alternative in this paper. The Kalman gain is replaced by a feedforward neural network whose weight adjustment permits minimization of the estimation error. The estimator has the capability of estimating the states of the plant in a stochastic environment without knowledge of noise statistics. If the noise of the plant is white and Gaussian and its statistics are well known, the neural estimator and the Kalman filter produce equally good results. The neural filtering approaches of colored noise based on the Kalman filter structure are applied to restore the cephalometric images of stomatology. Several experimental results demonstrate the feasibility and good performances of the approaches.
Keywords :
Gaussian noise; adaptive Kalman filters; feedforward neural nets; filtering theory; image denoising; image restoration; medical image processing; random noise; white noise; Gaussian white noise; Kalman filter structure; Kalman filtering model; Kalman gain; adaptive filtering; cephalometric image restoration; colored measurement noise; coloured noise; equivalent observation equation; estimation error minimization; feedforward neural network; measurement noise variance; neural estimator; observation correlation-based algorithm; shaping filter; single layer neural network; stochastic environment; stomatology; Adaptive filters; Colored noise; Equations; Filtering; Gaussian noise; Kalman filters; Neural networks; Noise measurement; Noise shaping; State estimation;
fLanguage :
English
Journal_Title :
Instrumentation and Measurement, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9456
Type :
jour
DOI :
10.1109/TIM.2003.814669
Filename :
1213656
Link To Document :
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