Image reconstruction algorithms for electrical capacitance tomography

Abstract

Electrical capacitance tomography (ECT) is used to image cross-sections of industrial processes containing dielectric material. This technique has been under development for more than a decade. The task of image reconstruction for ECT is to determine the permittivity distribution and hence material distribution over the cross-section from capacitance measurements. There are three principal difficulties with image reconstruction for ECT: (1) the relationship between the permittivity distribution and capacitance is non-linear and the electric field is distorted by the material present, the so-called 'soft-field' effect; (2) the number of independent measurements is limited, leading to an under-determined problem and (3) the inverse problem is ill posed and ill conditioned, making the solution sensitive to measurement errors and noise. Regularization methods are needed to treat this ill-posedness. This paper reviews existing image reconstruction algorithms for ECT, including linear back-projection, singular value decomposition, Tikhonov regularization, Newton-Raphson, iterative Tikhonov, the steepest descent method, Landweber iteration, the conjugate gradient method, algebraic reconstruction techniques, simultaneous iterative reconstruction techniques and model-based reconstruction. Some of these algorithms are examined by simulation and experiment for typical permittivity distributions. Future developments in image reconstruction for ECT are discussed.

An Image Reconstruction Algorithm for Electrical Impedance Tomography Using Adaptive Group Sparsity Constraint

“…The image reconstruction is performed using Matlab 2013a installed on a windows desktop with an Intel Xeon CPU (X5650 @ 2.67 GHz, 2 processors) and 24 GB memory. According to [21], the computation cost each iteration of the ADMM is O(mn) when applied to solve Eq. (13).…”

“…In addition, an open-source Matlab toolkit named EIDORS was developed and has been widely used for three-dimensional EIT image reconstruction problems in the past decades [20], which integrates the most commonly used EIT image reconstruction algorithms. Beyond that, the comprehensive review of the state-of-the-art EIT image reconstruction algorithms is also well summarized and thoroughly discussed in [21] and [22]. In spite of existing achievements, it is still highly requisite to develop EIT image reconstruction algorithms with higher spatial resolution and smaller image error for the purpose of high definition conductivity imaging.…”

Co-operative sensor fusion using time warping in multimodal tomometry for process control

“…where, ∆C is the change in capacitance, dξ dε is called the sensitivity of the capacitance against permittivity distribution, ∆ε is the change in permittivity distribution, Since, ∆ε is very small, the higher order terms of the equation, O((∆ε) 2 ) can be neglected (Yang & Peng 2003).…”

“…This process of calculating the inter-electrode capacitances from a known permittivity distribution is called as the forward problem. This is the linear approximation to the non linear forward problem (Yang & Peng 2003). Since the range of permittivity and capacitance values are very small, normalised form is used.…”

“…Simply, it can be explained as finding unknown K n from known c n in the Equation (2.7). But there are two main problems as explained in (Yang & Peng 2003). First one is, the number of unknowns are larger than the number of equations.…”