Low-Rank and Sparse Tensor Decomposition: Toward Real-Time Dynamic EIT Reconstruction

Electrical impedance tomography (EIT) is an emerging parameter visualization technology widely applied in industrial and medical scenarios. However, due to the limited of measurement signals and the “soft field” nature, the inverse problem of EIT exhibits severe ill-posedness and nonlinearity, which results in low resolution and obvious artifacts in reconstructed images especially in dynamic scenes. To enhance the performance of dynamic EIT, a tensor low-rank and sparse decomposition (TLSD) method is proposed for dynamic EIT reconstruction. The low-rank and sparse properties of dynamic EIT data are validated through singular value analysis of spatiotemporally coupled third-order tensors. The dynamic EIT tensor is decomposed into a low-rank component using tensor nuclear norm (TNN) based on tensor singular value decomposition (t-SVD) and a sparse feature with total p-variation (TpV) regularization. Furthermore, we propose an improved iterative solver within the dual alternating direction method of multipliers (D-ADMM) optimization framework. To validate the effectiveness of our proposed method, we established two phantom experiments and an in vivo task focusing on spatial and impedance resolution. Both visual reconstruction results and quantitative metrics demonstrate that our proposed TLSD method effectively incorporates temporal correlations between interslices while combining structural information within intraslices. Experimental analyses thoroughly validate the superiority of our TLSD method in dynamic EIT reconstruction, enabling dynamic parameter detection and complex process visualization tasks.