A Feasibility Study of 2-D Microwave Thorax Imaging Based on the Supervised Descent Method

In this paper, the application of the supervised descent method (SDM) for 2-D microwave thorax imaging is studied. The forward modeling problem is solved by the finite element-boundary integral (FE-BI) method. According to the prior information of human thorax, a 3-ellipse training set is generated offline. Then, the average descent direction between an initial background model and the training models is calculated. Finally, the reconstruction of the testing thorax model is achieved based on the average descent directions online. The feasibility using One-Step SDM for thorax imaging is studied. Numerical results indicate that the structural information of thorax can be reconstructed. It has potential for real-time imaging in future clinical diagnosis.

Application of supervised descent method for 2D magnetotelluric data inversion

The supervised descent method (SDM) is applied to 2D magnetotellurics (MT) data inversion. SDM contains offline training and online prediction. The training set is composed of the models generated according to prior knowledge and the data simulated by MT forward modeling. In the training process, a set of descent directions from an initial model to the training models is learned. In the prediction, model reconstruction is achieved by optimizing an online regularized objective function with a restart scheme, where the learned descent directions and the computed data residual are involved. SDM inversion has the advantages of (1) being more efficient than traditional gradient-descent methods because the computation of local derivatives of the objective function is avoided, (2) incorporating prior uncertain knowledge easier than deterministic inversion approach by generating training models flexibly, and (3) having high generalization ability because the physical modeling can guide the online model reconstruction. Furthermore, a way of designing general training set is introduced, which can be used for training when the prior knowledge is weak. The efficiency and accuracy of this method are validated by two numerical examples. The results indicate that the reconstructed models are consistent with prior information, and the simulated responses agree well with the data. This method also shows good potential to improve the accuracy and efficiency in field MT data inversion.