Registered Data

[CT032]

  • Session Time & Room
    • CT032 (1/1) : 2C @G601 [Chair: Ray-Hon Sun]
  • Classification
    • CT032 (1/1) : Elliptic equations and elliptic systems (35J)

[01233] A Study of the Spectra-Cutoff Imaging Method of Multiple Scattering in Isotropic Point-Like Discrete Random Media

  • Session Time & Room : 2C (Aug.22, 13:20-15:00) @G601
  • Type : Contributed Talk
  • Abstract : Imaging in random media is an important and interesting subject of inverse problems, relevant to a wide range of physical and engineering contexts, such as seismic imaging, remote sensing, medical imaging, wireless communications, and nondestructive testing. In this talk, we show that imaging becomes difficult to perform in random media when multiple scattering is too strong to cause image distortion arising from the underlying interactions of multiply scattered waves at resonance frequencies. The Foldy-Lax-Lippmann-Schwinger, (FLLS), formalism, which is employed for the multiply scattered waves, in the frequency domain, in the case of an ensemble of randomly distributed point-like scatterers. The scattering matrix representing the (FLLS) formalism is a non-Hermitian Euclidean random matrix. According to the eigenvalue distribution of the scattering matrix, we present our approach to restore the distorted images by cutting off the sharp frequency responses in the resonance regime due to strong multiple scattering. Finally, we show the use of this approach for imaging in discrete random media with numerical simulations and also discuss the limitations and future research direction.
  • Classification : 35J05, 35P15, 35P25, 47B06, 78A46
  • Format : Talk at Waseda University
  • Author(s) :
    • Ray-Hon Sun (Stanford University (while working on this research))

[00958] Existence results and numerical approximation for a quasilinear elliptic system

  • Session Time & Room : 2C (Aug.22, 13:20-15:00) @G601
  • Type : Contributed Talk
  • Abstract : We analyse, in the context of anisotropic Sobolev spaces, the existence and the numerical simulation of a capacity solution to a coupled nonlinear elliptic system. We consider the case of a non-uniformly elliptic problem with a quadratic growth in the gradient. The system may be regarded as a generalization of the so-called thermistor problem.
  • Classification : 35J47, 35J70, 47H05, 46E35, 65N12
  • Format : Online Talk on Zoom
  • Author(s) :
    • Hajar Talbi (Moulay Ismail University)
    • Mohamed Rhoudaf (Moulay Ismail University)
    • Francisco Ortegón Gallego (Universidad de Cádiz)

[01754] Spectral-Cutoff for Imaging of Multiple Scattering in Isotropic Point-Like Discrete Random Media

  • Session Time & Room : 2C (Aug.22, 13:20-15:00) @G601
  • Type : Contributed Talk
  • Abstract : To image objects in the discrete random medium composed of isotropic point-like scatterers, the resonances with multiple scattering in the medium can interfere with imaging and result in poor quality of images. To solve this problem, we present a spectral-cutoff method, which is derived based on the random matrix theory, to filter out the undesired responses in the resonance regime to recover the damaged images. Finally, we demonstrate this method for boosting imaging with numerical simulations.
  • Classification : 35J05, 35P15, 47B06, 78A46, 94A12
  • Author(s) :
    • Ray-Hon Sun (Stanford University)
    • Ray-Hon Sun (Stanford University)