6 research outputs found
Lam\'e Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
We consider a problem of quantitative static elastography, the estimation of
the Lam\'e parameters from internal displacement field data. This problem is
formulated as a nonlinear operator equation. To solve this equation, we
investigate the Landweber iteration both analytically and numerically. The main
result of this paper is the verification of a nonlinearity condition in an
infinite dimensional Hilbert space context. This condition guarantees
convergence of iterative regularization methods. Furthermore, numerical
examples for recovery of the Lam\'e parameters from displacement data
simulating a static elastography experiment are presented.Comment: 29 page
Limited Angle Acousto-Electrical Tomography
This paper considers the reconstruction problem in Acousto-Electrical
Tomography, i.e., the problem of estimating a spatially varying conductivity in
a bounded domain from measurements of the internal power densities resulting
from different prescribed boundary conditions. Particular emphasis is placed on
the limited angle scenario, in which the boundary conditions are supported only
on a part of the boundary. The reconstruction problem is formulated as an
optimization problem in a Hilbert space setting and solved using Landweber
iteration. The resulting algorithm is implemented numerically in two spatial
dimensions and tested on simulated data. The results quantify the intuition
that features close to the measurement boundary are stably reconstructed and
features further away are less well reconstructed. Finally, the ill-posedness
of the limited angle problem is quantified numerically using the singular value
decomposition of the corresponding linearized problem.Comment: 23 page
Levenberg-Marquardt algorithm for acousto-electric tomography based on the complete electrode model
The inverse problem in Acousto-Electric tomography concerns the
reconstruction of the electric conductivity in a domain from knowledge of the
power density function in the interior of the body. This interior power density
results from currents prescribed at boundary electrodes (and can be obtained
through electro-static boundary measurements together with auxiliary acoustic
measurement. In Electrical Impedance Tomography, the complete electrode model
is known to be the most accurate model for the forward modelling. In this
paper, the reconstruction problem of Acousto-Electric tomography is posed using
the (smooth) complete electrode model, and a Levenberg-Marquardt iteration is
formulated in appropriate function spaces. This results in a system of partial
differential equations to be solved in each iteration. To increase the
computational efficiency and stability, a strategy based on both the complete
electrode model and the continuum model with Dirichlet boundary condition is
proposed. The system of equations is implemented numerically for a two
dimensional scenario and the algorithm is tested on two different numerical
phantoms, a heart and lung model and a human brain model. Several numerical
experiments are carried out confirming the feasibility, accuracy and stability
of the methods
Quantitative PAT-OCT Elastography for Biomechanical Parameter Imaging
Diseases like cancer or arteriosclerosis often cause changes of tissue stiffness in the micrometer scale. Our work aims at developing a non-invasive method to quantitatively image these biomechanical changes and study the potential of the method for medical diagnostics. We focus on quantitative elastography combined with photoacoustic (PAT) and optical coherence tomography (OCT). The problem we deal with consists in estimating elastic material parameters from internal displacement data, which are evaluated from OCT-PAT recordered successive images of a sample.Non UBCUnreviewedAuthor affiliation: University of ViennaPostdoctora