EST image reconstruction based on primal dual interior point algorithm

The passive induction mechanism of electrostatic tomography (EST) determines that the number of independent measurements is equal to the number of electrodes, which is much less than the number of independent measurements of relatively mature electrical tomography (ET) technologies such as elelctrical capacitance tomography (ECT), resulting in a more severe underdetermined inverse problem. In order to address this problem, compressed sensing-based EST image reconstruction algorithm is studied. The sensitivity matrix is processed by singular value decomposition (SVD) to satisfy the restricted isometry property (RIP), and thereafter the l₁ norm regularization model and primal dual interior point algorithm (PDIPA) are utilized to reconstruct the image. Besides, constraint on the number of non-zero elements in the image vector is imposed in the iteration process according to the sparsity of debris distributed in oil. Simulation experiment demonstrates that compared to the "Circle of Appolonius" based back-projection (BP) algorithm and Landweber iteration algorithm, the aforementioned algorithm has obviously improved the imaging quality:accurate reconstruction can be obtained for single charge distributed at different positions; for two point charges whose distance is more than or equal to 1 mm, both the number and positions of the point charges can be correctly observed; for 10 groups of three randomly distributed point charge models, the accuracy rate of charged debris number monitoring is about 80%.