Numerical reconstruction for 3D nonlinear SAR imaging via a version of the convexification method

TL;DR

This paper extends a convexification-based algorithm for 3D nonlinear SAR imaging to detect explosive-like targets, demonstrating its effectiveness through numerical tests without relying on linearization.

Contribution

It introduces a 3D numerical reconstruction method for nonlinear SAR imaging using convexification, applicable to detecting buried explosive targets, and verifies its global convergence.

Findings

Successfully reconstructs 3D dielectric images from simulated data.

Demonstrates the method's global convergence in numerical tests.

Effective for detecting explosive-like targets in non-invasive inspections.

Abstract

This work extends the applicability of our recent convexification-based algorithm for constructing images of the dielectric constant of buried or occluded target. We are orientated towards the detection of explosive-like targets such as antipersonnel land mines and improvised explosive devices in the non-invasive inspections of buildings. In our previous work, the method is posed in the perspective that we use multiple source locations running along a line of source to get a 2D image of the dielectric function. Mathematically, we solve a 1D coefficient inverse problem for a hyperbolic equation for each source location. Different from any conventional Born approximation-based technique for synthetic-aperture radar, this method does not need any linearization. In this paper, we attempt to verify the method using several 3D numerical tests with simulated data. We revisit the global convergence of the gradient descent method of our computational approach.