Multitransmitter Sparse Inversion Algorithm for Reconstruction of Nonsparse Perfect Electric Conductors

In this article, a novel linear and efficient multitransmitter sparse inversion algorithm, termed Multitask Focal Underdetermined System Solver (MT-FOCUSS), is proposed and first extended to the reconstruction of nonsparse perfect electric conductors (PECs) by determining the intensity of induced currents. To overcome the ill-posedness of inverse problems, the multitask sparsity measure is defined. This measure not only considers the correlation of induced currents under different transmitters but also reduces the reliance on the sparsity of the target. The two key characteristics enable accurate reconstruction of nonsparse PEC scatterers, including multiple or concave scatterers, even electrically large ones. In addition, the regularization parameter is carefully chosen to better accommodate various signal-to-noise ratios (SNRs). The reconstruction accuracy, noise robustness, and computational efficiency of the proposed method are validated and assessed against synthetic and experimental data. Comparative analysis with sparse algorithms and other conventional algorithms backprojection algorithm (BPA) and subspace-based optimization method (SOM) further demonstrates the advantages of the proposed MT-FOCUSS.