@article{gilman_smith_tsynkov_2014, title={Single-polarization SAR imaging in the presence of Faraday rotation}, volume={30}, ISSN={0266-5611 1361-6420}, url={http://dx.doi.org/10.1088/0266-5611/30/7/075002}, DOI={10.1088/0266-5611/30/7/075002}, abstractNote={We discuss the single-polarization SAR imaging with the Faraday rotation (FR) taken into account. The FR leads to a reduction in the intensity of the received radar signal that varies over the signal length. That, in turn, results in a degradation of the image. In particular, the image of a point target may have its intensity peak split in the range direction. To distinguish between the cases of low reflectivity and those where the low antenna signal is due to the FR, we employ the image autocorrelation analysis. This analysis also helps determine the parameters of the FR, which, in turn, allow us to introduce an approach for correcting the single-polarization SAR images distorted by FR.}, number={7}, journal={Inverse Problems}, publisher={IOP Publishing}, author={Gilman, Mikhail and Smith, Erick and Tsynkov, Semyon}, year={2014}, month={Jun}, pages={075002} }
 @article{gilman_smith_tsynkov_2013, title={Reduction of ionospheric distortions for spaceborne synthetic aperture radar with the help of image registration}, volume={29}, ISSN={0266-5611 1361-6420}, url={http://dx.doi.org/10.1088/0266-5611/29/5/054005}, DOI={10.1088/0266-5611/29/5/054005}, abstractNote={We propose a robust technique for reducing the ionospheric distortions in spaceborne synthetic aperture radar (SAR) images. It is based on probing the terrain on two distinct carrier frequencies. Compared to our previous work on the subject (Smith and Tsynkov 2011 SIAM J. Imaging Sciences 4 501–42), the increase in robustness is achieved by applying an area-based image registration algorithm to the two images obtained on two frequencies. This enables an accurate evaluation of the shift between the two images, which, in turn, translates into an accurate estimate of the total electron content and its along-track gradient in the ionosphere. These estimates allow one to correct the matched filter and thus improve the quality of the image. Moreover, for the analysis of SAR resolution in the current paper we take into account the Ohm conductivity in the ionosphere (in addition to its temporal dispersion), and also consider the true Kolmogorov spectrum of the ionospheric turbulence, as opposed to its approximate representation that we have used previously.}, number={5}, journal={Inverse Problems}, publisher={IOP Publishing}, author={Gilman, Mikhail and Smith, Erick and Tsynkov, Semyon}, year={2013}, month={Apr}, pages={054005} }
 @article{gilman_smith_tsynkov_2012, title={A linearized inverse scattering problem for the polarized waves and anisotropic targets}, volume={28}, ISSN={0266-5611 1361-6420}, url={http://dx.doi.org/10.1088/0266-5611/28/8/085009}, DOI={10.1088/0266-5611/28/8/085009}, abstractNote={We analyze the scattering of a plane transverse linearly polarized electromagnetic wave off a plane interface between the vacuum and a given material. For a variety of predominantly dielectric materials, from isotropic to anisotropic and weakly conductive, we show that when the scattering is weak, the first Born approximation predicts the correct scattered field in the vacuum region. We also formulate and solve the corresponding linearized inverse scattering problem. Specifically, we provide a necessary and sufficient condition under which interpreting the target material as a weakly conductive uniaxial crystal allows one to reconstruct all the degrees of freedom contained in the complex 2 × 2 Sinclair scattering matrix. This development can help construct a full-fledged radar ambiguity theory for polarimetric imaging by means of a synthetic aperture radar (SAR), which is in contrast to the approach that currently dominates the SAR literature and exploits a fully phenomenological scattering matrix. Moreover, the linearized scattering off a material half-space naturally gives rise to the ground reflectivity function in the form of a single layer (i.e. a δ-layer) at the interface. A ground reflectivity function of this type is often introduced in the SAR literature without a rigorous justification. Besides the conventional SAR analysis, we expect that the proposed approach may appear useful for the material identification SAR (miSAR) purposes.}, number={8}, journal={Inverse Problems}, publisher={IOP Publishing}, author={Gilman, Mikhail and Smith, Erick and Tsynkov, Semyon}, year={2012}, month={Jul}, pages={085009} }
 @article{smith_tsynkov_2011, title={Dual Carrier Probing for Spaceborne SAR Imaging}, volume={4}, ISSN={1936-4954}, url={http://dx.doi.org/10.1137/10078325X}, DOI={10.1137/10078325x}, abstractNote={Spaceborne imaging of the Earth's surface by synthetic aperture radar (SAR) may be adversely affected by the ionosphere that causes distortions of the signals emitted and received by the radar antenna. In our previous publication on the subject [SIAM J. Imaging Sci., 2 (2009) pp. 140-182], we have analyzed those distortions for the inhomogeneous ionosphere described by the cold plasma model. Based on the analysis, we have concluded that the deterioration of SAR images was due to the mismatch between certain parameters of the actual received signal, which is slowed down by the temporal dispersion in the ionosphere, and the corresponding parameters of the matched filter, which is taken as if the propagation were unobstructed. Consequently, to improve the quality of the images, the filter must be corrected. However, to get the appropriate correction, one needs to know some key characteristics of the ionosphere precisely at the time and place the image is taken. To obtain those characteristics, we currently propose probing the terrain, and hence the ionosphere, on two distinct carrier frequencies. We also investigate the performance of the matched filters that were corrected this way and show that the final quality of the images, i.e., their resolution and sharpness evaluated using the SAR ambiguity theory, indeed improves.}, number={2}, journal={SIAM Journal on Imaging Sciences}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Smith, E. M. and Tsynkov, S. V.}, year={2011}, month={Jan}, pages={501–542} }