Deep Learning Based Electromagnetic Source Imaging Method Using Deep Convolutional Conditional Denoising Diffusion Probabilistic Model

In this work, we introduce an electromagnetic source imaging (EMSI) approach utilizing deep learning (DL) techniques, which employs deep convolutional conditional denoising diffusion probabilistic model (DCCDDPM). Conventional EMSI methods often struggle with various challenges, such as low accuracy and ill-posedness. The newly proposed EMSI method, named as DCCDDPM-EMSI, includes the forward diffusion process and the reverse diffusion process. Its diffusion process starts with EM equivalent sources on targets and adds Gaussian noise in a series of steps. On the counterpart, its reverse diffusion process step-by-step predicts the noise by using DL-based noise prediction network combined with the EM scattering measurements as conditional inputs. In contrast to traditional DDPM frame, the proposed DCCDDPM-EMSI introduces model-based loss term, which measures the discrepancy between the true EM sources and those predicted ones, in the diffusion process during its training process. Consequently, the proposed DCCDDPM-EMSI can reconstruct EM equivalent source of targets from the measured EM scattered field data. Unlike conventional EMSI methods, DCCDDPM-EMSI allows for higher fidelity EM source reconstruction without incurring excessive computational cost. Numerical benchmarks demonstrate that DCCDDPM-EMSI cannot only ensure the high accuracy but also the excellent generality, which offers significant advancements for DL-inspired quantitative EM imaging.