Multitask Bayesian Compressive Sensing for Phaseless Electromagnetic Inverse Problems

Electromagnetic (EM) inverse problems have always been an important research topic in applied electro-magnetics. They have great application values in EM characterization and inverse design by reconstructing unknown EM parameters from measured or user-defined EM field information. Some typical problems include inverse scattering, inverse source reconstruction, antenna array synthesis, fault diagnosis, and direction-of-arrival (DoA) estimation. In recent years, the compressive sensing (CS) technique has shown great potential in solving EM inverse problems. It allows faithful reconstruction from undersampled measurements by exploiting the sparse property of EM parameters, thus leading to significant improvement in efficiency and accuracy of reconstructions. The Bayesian compressive sensing (BCS) algorithm, based on a probabilistic CS framework, does not rely on inconvenient Restricted Isometry Property (RIP) verifications to yield stable results. It is preferred in EM problems where the RIP conditions are hardly satisfied.