An optimized Tikhonov regularization algorithm for EIT image reconstruction

In the electrical impedance imaging (EIT) problem, aiming at the problem that the traditional Tikhonov regularization algorithm uses a single L2 norm as the regularization term, which leads to the over-smoothing of the solution and the unclear reconstruction of the image, this paper proposes an iterative Tikhonov algorithm (MLTR) with multiple regularization as the penalty term and logarithmic weight factor solving. At the same time, the regularization matrix is modified to improve the lack of prior information caused by the traditional use of the identity matrix as the regularization matrix. Finally, in order to reduce the corresponding time and computational complexity, the dimensionality of MLTR algorithm reconstruction is reduced. Compared with traditional Tikhonov algorithm and iterative algorithms such as Land Weber and conjugate gradient (CG), MLTR algorithm has obvious improvement in imaging clarity and boundary artifacts. The relative error RIE of reconstructed images is as low as 0.0564, and the imaging time is significantly shortened after dimensionality reduction.