Non-zero constraints in elliptic PDE with random boundary values and applications to hybrid inverse problems

Abstract

Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving the unknown parameters and some related quantities are obtained, and, second, the unknown parameters have to be reconstructed from the internal data. The reconstruction in the second step requires the solutions of certain PDE to satisfy some non-zero constraints, such as the absence of nodal or critical points, or a non-vanishing Jacobian.

Document Details

Document Type
Pub Defense Publication
Publication Date
Oct 28, 2022
Source ID
10.1088/1361-6420/ac9924

Entities

People

  • Giovanni S. Alberti

Organizations

  • Air Force Office of Scientific Research

Tags

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.
  • Image Processing and Computer Vision.