Image Reconstruction Algorithm Based On PCA and WNN for ECT

Image Reconstruction Algorithm Based On PCA and WNN for ECT

Lifeng Zhang (Department of Automation, North China Electric Power University, Baoding, China)
DOI: 10.4018/ijapuc.2013100103
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Abstract

Electrical capacitance tomography (ECT) technique is a new technique for two-phase flow measurement. ECT is a complex nonlinear problem. To solve the ill-posed image reconstruction problem, image reconstruction algorithm based on wavelet neural networks (WNN) was presented. The principal component analysis (PCA) method was used to reduce the dimension of the input vectors. The transfer functions of the neurons in the WNN were wavelet base functions which were determined by retract and translation factors. The input measurement data were obtained using the ECT simulation software developed by the author. BP algorithm was used to train the WNN, and self-adaptive learning rate and momentum coefficient were also used to accelerate the learning speed. Experimental results showed the image quality has been improved markedly, compared with the typical linear back projection (LBP) algorithm and Landweber iteration algorithm.
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1. Introduction

Tomography can be described as the measurement of some characteristic by examining it in cross-section. A tomographic reconstruction of the cross-section of a vessel can be achieved using a variety of measurement variables, including resistance, capacitance and mutual inductance. Electrical capacitance tomography (ECT) was one of the most developed electrical tomography techniques, which was firstly designed for monitoring process applications. It offers some advantages over some other tomography techniques, such as low cost, no radiation and being no-invasive and has gained considerable momentum in recent years (Liu et al., 2001; York, 2001; Zhu et al., 2003).

This technique involves a number of capacitive electrodes mounted circumferentially on pipe, as shown in Figure 1, and relies on changes in capacitance values between electrodes owing to the change of permittivity for flow components.

Figure 1.

Principle diagram of ECT system

Capacitances are measured between different combination electrode pairs and the obtained data are used to reconstruct cross sectional distribution of flow components. ECT is composed of forward problem and inverse problem (Yang & Peng, 2003). The inverse problem is also called image reconstruction. Linear back projection algorithm is often used for image reconstruction of ECT for its fast speed, but the reconstruction images obtained by this algorithm have relatively low accuracy. In order to analyze two-phase flow system better, there is an urgent need for development of the image reconstruction algorithm with higher accuracy.

The ability of nonlinear approximation of WNN models has been shown by many researchers (Hossen, 2004; Zhang, 1992). Combining the ability of wavelet transformation for revealing the property of function in localize region with learning ability and general approximation properties of neural network, different types of wavelet neural networks (WNNs) have been proposed, which is suitable for the approximation of unknown nonlinear functions with local nonlinearities and fast variations because of its intrinsic properties of finite support and self-similarity (Banakar & Azeem, 2008; Zhang et al., 1995).

The main contribution of this paper is to propose the image reconstruction algorithm based on WNNs for ECT. The dimension of the inputs was reduced using PCA method. Simulation results showed image quality has been improved markedly, compared with the typical linear back projection (LBP) algorithm and Landweber iteration algorithm.

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