Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging
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 parametriz...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/9/12/2055 |
| _version_ | 1797545845554413568 |
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| author | Gabriele Incorvaia Oliver Dorn |
| author_facet | Gabriele Incorvaia Oliver Dorn |
| author_sort | Gabriele Incorvaia |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T14:20:49Z |
| format | Article |
| id | doaj.art-d7cfc33e612746baa0ca8052648a024f |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T14:20:49Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-d7cfc33e612746baa0ca8052648a024f2023-11-20T23:24:13ZengMDPI AGElectronics2079-92922020-12-01912205510.3390/electronics9122055Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar ImagingGabriele Incorvaia0Oliver Dorn1Department of Mathematics, The University of Manchester, Manchester M13 9PL, UKDepartment of Mathematics, The University of Manchester, Manchester M13 9PL, UKIn 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.https://www.mdpi.com/2079-9292/9/12/2055first and second order stochastic optimization algorithmsstochastic shape evolutionparametrised level set functionsthrough-the-wall radar imaginginverse problems |
| spellingShingle | Gabriele Incorvaia Oliver Dorn Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging Electronics first and second order stochastic optimization algorithms stochastic shape evolution parametrised level set functions through-the-wall radar imaging inverse problems |
| title | Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging |
| title_full | Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging |
| title_fullStr | Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging |
| title_full_unstemmed | Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging |
| title_short | Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging |
| title_sort | stochastic optimization methods for parametric level set reconstructions in 2d through the wall radar imaging |
| topic | first and second order stochastic optimization algorithms stochastic shape evolution parametrised level set functions through-the-wall radar imaging inverse problems |
| url | https://www.mdpi.com/2079-9292/9/12/2055 |
| work_keys_str_mv | AT gabrieleincorvaia stochasticoptimizationmethodsforparametriclevelsetreconstructionsin2dthroughthewallradarimaging AT oliverdorn stochasticoptimizationmethodsforparametriclevelsetreconstructionsin2dthroughthewallradarimaging |