Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging

Abstract

In this paper, a comparison of stochastic optimization algorithms is presented for the reconstruction of electromagnetic profiles in through-the-wall radar imaging. We combine those stochastic optimization approaches with a shape-based representation of unknown targets which is based on a parametrized level set formulation. This way, we obtain a stochastic version of shape evolution with the goal of minimizing a given cost functional. As basis functions, we consider in particular Gaussian and Wendland radial basis functions. For the optimization task, we consider three variants of stochastic approaches, namely stochastic gradient descent, the Adam method as well as a more involved stochastic quasi-Newton scheme. A specific backtracking line search method is also introduced for this specific application of stochastic shape evolution. The physical scenery considered here is set in 2D assuming TM waves for simplicity. The goal is to localize and characterize (and eventually track) targets of interest hidden behind walls by solving the corresponding electromagnetic inverse problem. The results provide a good indication on the expected performance of similar schemes in a more realistic 3D setup.

Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

“…. N. The ψ j (r) are often taken to be RBFs [21,26,36,47,49,50,56,64]. We will refer to use of such basis functions as "traditional PaLS," and it is against such representations that we compare our new PaLEnTIR representation.…”

“…Moreover, it was shown in [2] that the low order representation of the inverse problem makes it possible to use Newton and quasi-Newton methods for determining the PaLS parameters. In recent work, the PaLS model in [2] and variants have been used across a range of application areas and imaging modalities including geophysics [52,53] and reservoir monitoring [34,35], image segmentation [54], acoustic scattering [21], dynamic tomography [56], dual-energy computed tomography [64], electrical impedance tomography [49,50], electromagnetic imaging [36], electrical capacitance tomography [47], and multi-modal imaging [26].…”

“…A second area of limitation for PaLS concerns the family of basis functions used to model the level set function. In a traditional PaLS setting, the level set function is obtained using a weighted superposition of a set of predetermined collection of basis functions, most often radial basis functions (RBFs) [21,36,47,49,50,56,64] but also polynomials [40], multiquadrics [54], ellipsoidal [26], and polytopes [54]. We focus here on RBFs due to their prevalence as well as a some nice properties specifically of compactly supported RBFs [2].…”

A Deep Learning-Based Electromagnetic Signal for Earthquake Magnitude Prediction

“…And before data input into each layer, we normalized the data of each channel after flattening, as follows: where is the flattened tensor when the channel dimension equals , and , and are the length, mean and standard deviation of , respectively. An Adam optimizer was applied with default values of parameters recorded in [ 49 ], and the mini-batch size was set as 128. The training data were shuffled for every epoch, and each network was trained for enough epochs about 200.…”

Resolving full-wave through-wall transmission effects in multi-static synthetic aperture radar

“…acoustic or elastic wave equation, Maxwell's equations, etc) is used in a reconstruction method such as regularised least-squares or Bayesian inversion, have now been widely employed for many inverse scattering problems, in particular for geophysical imaging [47,49] and the related ground-penetrating radar (GPR) problem [25,32,44,48]. For through-wall radar, full-wave inversion approaches have been applied in conjunction with level-set techniques both for 2D [26,28] and 3D image formation [27, chapter 3]. In both of these cases the wall was assumed known (which is reasonable), and somewhat complete data coverage of transmitter/receiver antennas surrounding the building in the near-field was simulated.…”