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

Wenjing Shang,Weizhi Geng,Wei Xue,Yidong Xu

doi:10.1109/access.2019.2954293

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.

Highlights

In the context of undersea exploration, such as submarine optical fiber imaging and dangerous object detection beneath the seabed, it is important to recover the 3D image of the target
To analyze the performance of detecting the boundary, we investigate the effect of the regularization terms with different regularization parameters β0∗ and β2∗, which is shown in Figure 6. β0∗ and 0 are the initial minimum gradient support (MGS) regularization parameter and model misfit, respectively; β2∗ and 2 are the initial LoG regularization parameter and model misfit, respectively
We propose a novel inversion method based on the LoG operator and MGS regularization for reconstructing sharp-boundary targets buried beneath the seabed

Summary

INTRODUCTION

In the context of undersea exploration, such as submarine optical fiber imaging and dangerous object detection beneath the seabed, it is important to recover the 3D image of the target. The TV regularization method is not differentiable at zero, restricting its application To overcome this drawback, Acar and Vogel propose the modified-TV model [20] by introducing a small number. To further improve the reconstruction of a blocky target beneath the seabed, we propose a two-stage inversion method based on the 3D LoG function and the MGS model. A(σ ) is defined as the forward model that relates to the given conductivity σ It can be expressed by using the divergence matrix and the gradient:. Solving (5) involves a nonlinear ill-posed problem, resulting in unstable and non-unique inversion results It is possible for several different models to fit the observed data with the same accuracy. Ajo-Franklin suggests fixing ε at a reasonable value determined by experience [30]

THE LOG CONVOLUTION KERNEL-BASED REGULARIZATION ITEM IN 3D SPACE

THE GAUSS-NEWTON METHOD

THE LOG-MGS INVERSION STRATEGY

THE REGULARIZATION PARAMETERS

Findings

CONCLUSION