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Open Access Publications from the University of California

Scholarly Works (23 results)

  • Article
  • Peer Reviewed
UC Merced Previously Published Works (2023)
Abstract: We study the effects of absorption in the medium on synthetic aperture imaging. We model absorption using the loss tangent, which is the imaginary part of the relative dielectric permittivity, and study two cases: (i) the loss tangent is known and (ii) the loss tangent is unknown. When the loss tangent is known and used in Kirchhoff migration (KM), we find that images of targets are range-shifted by approximately a central wavelength so that their predicted locations are closer to the synthetic aperture than they actually are. In contrast, we find that when the medium is unknown, the KM image does not exhibit this range-shift. Hence, we determine that it is better to not make use of any knowledge of the absorption when imaging. Using a recently developed transformation of KM images, which we call reciprocal-KM (rKM), we achieve tunably high-resolution images of targets through adjusting the value of a user-defined parameter ε. When rKM is applied to an imaging region containing two targets, we find that their predicted locations shift, especially in range, but within a fraction of central wavelength of their true locations.
    Creative Commons 'BY' version 4.0 license
    • Article
    • Peer Reviewed
    UC Merced Previously Published Works (2023)
      Cover page: Synthetic Aperture Imaging of Dispersive TargetsCreative Commons 'BY' version 4.0 license
      • Thesis
      • Peer Reviewed
      UC Merced Electronic Theses and Dissertations (2011)

      We study two methods to analyze spatio-temporal data. To describe data, we use principal component analysis. To predict data, we use dynamic mode decomposition. We compute numerical solutions of the complex Ginzburg-Landau equation and we use that numerical solution as data. Using principal component analysis we identify a low-dimensional subspace spanned by only 3 principal components. Using these 3 principal components we can reconstruct the original data matrix with approximately 2% error, and construct out-of-sample data with less than 3% error. Using dynamic mode decomposition we are able to predict the temporal evolution of out-of-sample data as far as 500 time steps into the future with less than 5% error. The combination of these two techniques provides robust and reliable methods to analyze complex data sets.

        Cover page: Using principal component analysis and dynamic mode decomposition to analyze spatio-temporal data
        • Article
        • Peer Reviewed
        UC Merced Previously Published Works (2019)
        We present a method for inverse scattering that relies on intensity-only measurements of the scattered field on a single measurement plane. By collecting measurements from a suite of experiments in which the sample is illuminated using different incident fields, we create sufficient data diversity to overcome the limitations of the intensity-only measurements. We give an explicit procedure that uses an algebraic relation called the polarization identity to convert intensity measurements of scattered fields to interferometric measurements in which one of the scattered fields serves as the reference. By adjusting the multiple signal classification (MUSIC) method for these interferometric data, we effectively recover the location and shapes of multiple objects contained in the imaging region. This method is effective and robust to noise as long as there is sufficiently high data diversity and the fractional volume of the scattering objects is not too high. We present image reconstructions for several three-dimensional examples with simulated data computed using the Method of Fundamental Solutions that demonstrate the effectiveness of this imaging method.
          Cover page: Intensity-only inverse scattering with MUSIC.
          • Article
          UC Merced Previously Published Works (2023)
          Motivated by applications in unmanned aerial based ground penetrating radar for detecting buried landmines, we consider the problem of imaging small point like scatterers situated in a lossy medium below a random rough surface. Both the random rough surface and the absorption in the lossy medium significantly impede the target detection and imaging process. Using principal component analysis we effectively remove the reflection from the air-soil interface. We then use a modification of the classical synthetic aperture radar imaging functional to image the targets. This imaging method introduces a user-defined parameter, δ, which scales the resolution by √δ allowing for target localization with sub wavelength accuracy. Numerical results in two dimensions illustrateWe study imaging methods for identifying point targets in a lossy medium below a random rough surface. the robustness of the approach for imaging multiple targets. However, the depth at which targets are detectable is limited due to the absorption in the lossy medium.
            Cover page: Synthetic aperture radar imaging below a random rough surfaceCreative Commons 'BY' version 4.0 license
            • Article
            UC Merced Previously Published Works (2023)
            We introduce a dispersive point target model based on scattering by a particle in the far-field. The synthetic aperture imaging problem is then expanded to identify these targets and recover their locations and frequency dependent reflectivities. We show that Kirchhoff migration (KM) is able to identify dispersive point targets in an imaging region. However, KM predicts target locations that are shifted in range from their true locations. We derive an estimate for this range shift for a single target. We also show that because of this range shift we cannot recover the complex-valued frequency dependent reflectivity, but we can recover its absolute value and hence the radar cross-section (RCS) of the target. Simulation results show that we can detect, recover the approximate location, and recover the RCS for dispersive point targets thereby opening opportunities to classifying important differences between multiple targets such as their sizes or material compositions.
              Cover page: Synthetic aperture imaging of dispersive targetsCreative Commons 'BY' version 4.0 license
              • Article
              • Peer Reviewed
              UC Merced Previously Published Works (2017)
              We introduce a new model for multiple scattering of polarized light by statistically isotropic and mirror-symmetric particles, which we call the generalized Kubelka-Munk (gKM) approximation. It is obtained through a linear transformation of the system of equations resulting from applying the double spherical harmonics approximation of order one to the vector radiative transfer equation (vRTE). The result is a 32×32 system of differential equations that is much simpler than the vRTE. We compare numerical solutions of the vRTE with the gKM approximation for the problem in which a plane wave is normally incident on a plane-parallel slab composed of a uniform absorbing and scattering medium. These comparisons show that the gKM approximation accurately captures the key features of the polarization state of multiply scattered light. In particular, the gKM approximation accurately captures the complicated polarization characteristics of light backscattered by an optically thick medium composed of a monodisperse distribution of dielectric spheres over a broad range of sphere sizes.
                Cover page: Generalized Kubelka-Munk approximation for multiple scattering of polarized light.
                • Article
                • Peer Reviewed
                UC Merced Previously Published Works (2023)
                Abstract: Motivated by applications in unmanned aerial based ground penetrating radar for detecting buried landmines, we consider the problem of imaging small point like scatterers situated in a lossy medium below a random rough surface. Both the random rough surface and the absorption in the lossy medium significantly impede the target detection and imaging process. Using principal component analysis we effectively remove the reflection from the air‐soil interface. We then use a modification of the classical synthetic aperture radar imaging functional to image the targets. This imaging method introduces a user‐defined parameter, δ, which scales the resolution by allowing for target localization with sub wavelength accuracy. Numerical results in two dimensions illustrate the robustness of the approach for imaging multiple targets. However, the depth at which targets are detectable is limited due to the absorption in the lossy medium.
                  Cover page: Synthetic Aperture Radar Imaging Below a Random Rough SurfaceCreative Commons 'BY' version 4.0 license
                  • Thesis
                  • Peer Reviewed
                  UC Merced Electronic Theses and Dissertations (2024)

                  We explore mechanisms behind social media by leveraging diverse datasets to examine the intersection between users and language. Our exploration centers on understanding how demographics influence online behaviors, particularly in the context of high-engagement socio-political discourse (such as conversations surrounding #BlackLivesMatter) and the dissemination of misinformation related to COVID-19 on micro-blogging platforms. We aim to contribute insights for actionable strategies for promoting informed dialogue and combating misinformation, understand the complexities of online discourse, and shed light on the ways in which social identity shapes individuals' perceptions and participation in the digital realm.

                    Cover page: Characterizing Language & Users on Social MediaCreative Commons 'BY' version 4.0 license
                    • Article
                    • Peer Reviewed
                    UC Merced Previously Published Works (2018)
                      Cover page: Asymptotic analysis for close evaluation of layer potentials
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