A novel quasi-newton image reconstruction algorithm for electrical capacitance tomography system

To solve the electrical capacitance tomography(ECT) technology ldquosoft fieldrdquo effect and pathological problem, a quasi-Newton new algorithm for electrical capacitance tomography is presented. On the basis of analyzing ECT system measurement principle, constructing corrector formula of secant approximation algorithm in second-order information items of objective functions. The feasibility of using this algorithm for ECT problems is also discussed. It shows that it is easy to meet the convergence condition and error of image reconstruction is small. Experimental results and simulation data indicate that the algorithm can provide high quality images and favorable stabilization compared with LBP and conjugate gradient algorithms and this new algorithm presents a feasible and effective way to research on image reconstruction algorithm for electrical capacitance tomography system.

I. Introduction

Flow imaging is a new technique developed rapidly in recent years, which has great developmental potential and wide industrial application prospect'<“. ² Having many distinct advantages such as low cost, wide application field, simple structure, non-invade and better safety, Electrical Capacitance Tomography(ECT) has being the most popular research direction and the main development in flow imaging tcchniquel”. Due to ECT's inherent nonlinear characteristic, and the quantity of available independent measured capacitance values(projection data) is limited, much smaller than the pixel quantity needed for image reconstructing, no analytical solution exist for inverse problem. Meanwhile, because of the nonlinearity and “soft-field” effect, and because of ECT system's poor stability of solution and severe ill-condition caused by the error of measurement, it brings great difficulty to image reconstruction'f”. Image reconstruction algorithm has always been the main difficulty for practicing and further developing ECT tcchniquc'f”, exploring good image reconstruction algorithm is important. At present, common methods used in ECT image reconstruction include: linear back projection algorithm (LBP), regularization‘’”, Landweber iterative method!”, projected-Landweber method and conjugate gradient (CG) [10], etc. On the basis of describing ECT system measurement principle, this paper put forward a Quasi-Newton algorithm which will greatly improve the image reconstruction stability and quality. Experimental results show the effectiveness of the algorithm, for the reconstructed object that investigated in this paper, this algorithm obtains a better image quality than LBP and CG algorithm, thus provides a effective new method for ECT image reconstruction.