Imaging of permeability defect distribution by electromagnetic tomography with hybrid L1 norm and nuclear norm penalty terms

Electromagnetic tomography (EMT), with the advantages of being non-contact, non-invasiveness, low cost, simple structure, and fast imaging speed, is a multi-functional tomography technique based on boundary measurement voltages to image the conductivity distribution within the sensing field. EMT is widely used in industrial and biomedical fields. Currently, there are few studies on the application of EMT in magnetic permeability materials, which makes it difficult to obtain high-quality reconstructed images due to its own properties that lead to obvious attenuation of electromagnetic waves during propagation, as well as the ill-posed and ill-conditioned characteristics of EMT. In this paper, a multi-feature objective function integrating L2 norm regularization, L1 norm regularization, and low-rank norm regularization is proposed to solve the challenge of magnetic permeability material imaging. This approach emphasizes the smoothness and sparsity. The split Bregman algorithm is introduced to efficiently solve the proposed objective function by decomposing the complex optimization problem into several simple sub-task iterative schemes. In addition, a nine-coil planar array electromagnetic sensor was developed and a flexible modular EMT system was constructed. We use correlation coefficient and error coefficient as indicators to evaluate the performance of the proposed image reconstruction algorithm. The effectiveness of the proposed method in improving the reconstruction accuracy and robustness is verified through numerical simulations and experiments.