Undersea Target Reconstruction Based on Coupled Laplacian-of-Gaussian and Minimum Gradient Support Regularizations

Abstract

In this paper, a novel inversion method is proposed to recover the sharp boundary of blocky targets buried beneath the seabed with conductivities different from that of the background environment. This method is implemented by combining the Laplacian-of-Gaussian (LoG) function with minimum gradient support (MGS) regularization. A two-stage inversion strategy is introduced to obtain stable and sharp boundary inversion results. We first use the LoG operator in 3D space to obtain the profile of the target and then switch to LoG-MGS coupled regularized inversion to obtain the sharp boundary of the target. It is crucial to choose an appropriate regularization parameter adjustment strategy. We use a bounded function to adjust the regularization parameters during the inversion, which can balance the observation information and the a priori information in a reasonable interval. Theoretical analysis and numerical simulations are conducted and the recovered results demonstrate that the proposed inversion method has a better performance in recovering blocky targets than canonical regularization terms.