Abstract
Problem statement: Many problems in scientific computing can be formulated as inverse problem. A vast majority of these problems are ill-posed problems. In Electrical Charge Tomography (EChT), normally the sensitivity matrix generated from forward modeling is very ill-condition. This condition posts difficulties to the inverse problem solution especially in the accuracy and stability of the image being reconstructed. The objective of this study is to reconstruct the image cross-section of the material in pipeline gravity dropped mode conveyor as well to solve the ill-condition of matrix sensitivity. Approach: Least Square with Regularization (LSR) method had been introduced to reconstruct the image and the electrodynamics sensor was used to capture the data that installed around the pipe. Results: The images were validated using digital imaging technique and Singular Value Decomposition (SVD) method. The results showed that image reconstructed by this method produces a good promise in terms of accuracy and stability. Conclusion: This implied that LSR method provides good and promising result in terms of accuracy and stability of the image being reconstructed. As a result, an efficient method for electrical charge tomography image reconstruction has been introduced.
Highlights
Ill-posed problems are frequently encountered in the fields of science and engineering such as spectroscopy, seismography, medical imaging and tomography
The problem with Least Square (LS) method is no unique solution (Isa and Rahmat, 2009). These methods normally faced with ill-posed problem. This is because sensitivity matrix or coefficient matrix used in Electrical Charge Tomography (EChT) is ill-posed
The values are exponential increased whenever solution reached at data number 9-16
Summary
Ill-posed problems are frequently encountered in the fields of science and engineering such as spectroscopy, seismography, medical imaging and tomography. The term ill-posed was original introduced by Hadamard in the beginning of this century. Ill-posed problem means that small changes in the data cause arbitrarily large changes in the solution. This reflected in ill-conditioning of matrix of the discrete model. The theory of ill-posed problem is well developed in many literatures (Bertero et al, 1988; Hansen, 1992a; Tarantola, 2005). A classical example of an ill-posed problem is the Fredholm integral equation of the first kind with a square integrals kernel (Matsusaka and Masuda, 2003) as Eq 1: b
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