Graph-Based Regularization Robust Reconstruction of Electromagnetic Field Strength via Proximal-Splitting Algorithms

Assessing electromagnetic field strength (EMFS) is crucial for security, biomedicine, geophysics, and diverse industries. This paper focuses on EMFS sensing and presents efficient technical methods for predicting or reconstructing the two-dimensional distribution of EMFS in a region of interest from noisy sample observations on a limited set of measurement positions. The EMFS sensing task is initially framed as the reconstruction of signals on graphs and is subsequently reformulated into two optimization problems subject to inequality constraints. The first problem is convex, with the goal of minimizing the graph total-variation under empirical noise levels. Meanwhile, the second problem is nonconvex and aims to improve accuracy of EMFS reconstruction by minimizing a minimax-concave penalty. For these two optimization problems, we propose two effective problem-solving algorithms, respectively, based on proximal primal–dual splitting schemes. Numerical simulations demonstrate the potential of our EMFS techniques in rapidly and accurately reconstructing the EMFS.