Three-dimensional electrical capacitance tomography reconstruction by the Landweber iterative algorithm with fuzzy thresholding

The image reconstruction for electrical capacitance tomography is a non-linear, underdetermined and ill-posed inverse problem. It is difficult to obtain a reconstructed image with high quality, especially in the case of three-dimensional (3D) reconstruction. An iterative image reconstruction algorithm with fuzzy thresholding is proposed in this study. The threshold value in each iteration is generated by minimising the measure of fuzziness of current reconstructed image. The algorithm proposed is tested by the noise-free and the noise-contaminated capacitance data. Extensive computer simulations demonstrate that the fuzzy thresholding can reduce low grey-level artefacts effectively. As a result, the spatial error, volume error, permittivity error and scattered artefacts of the reconstructed image are reduced obviously; not only that, the number of iterations needed to obtain a good reconstruction result is decreased greatly. The result of 3D reconstruction of a H-shape object verifies the effectiveness of the fuzzy thresholding further.