3,349 research outputs found
Convergence and Stability of the Inverse Scattering Series for Diffuse Waves
We analyze the inverse scattering series for diffuse waves in random media.
In previous work the inverse series was used to develop fast, direct image
reconstruction algorithms in optical tomography. Here we characterize the
convergence, stability and approximation error of the serie
Parametric Level Set Methods for Inverse Problems
In this paper, a parametric level set method for reconstruction of obstacles
in general inverse problems is considered. General evolution equations for the
reconstruction of unknown obstacles are derived in terms of the underlying
level set parameters. We show that using the appropriate form of parameterizing
the level set function results a significantly lower dimensional problem, which
bypasses many difficulties with traditional level set methods, such as
regularization, re-initialization and use of signed distance function.
Moreover, we show that from a computational point of view, low order
representation of the problem paves the path for easier use of Newton and
quasi-Newton methods. Specifically for the purposes of this paper, we
parameterize the level set function in terms of adaptive compactly supported
radial basis functions, which used in the proposed manner provides flexibility
in presenting a larger class of shapes with fewer terms. Also they provide a
"narrow-banding" advantage which can further reduce the number of active
unknowns at each step of the evolution. The performance of the proposed
approach is examined in three examples of inverse problems, i.e., electrical
resistance tomography, X-ray computed tomography and diffuse optical
tomography
Quantitative photoacoustic imaging in radiative transport regime
The objective of quantitative photoacoustic tomography (QPAT) is to
reconstruct optical and thermodynamic properties of heterogeneous media from
data of absorbed energy distribution inside the media. There have been
extensive theoretical and computational studies on the inverse problem in QPAT,
however, mostly in the diffusive regime. We present in this work some numerical
reconstruction algorithms for multi-source QPAT in the radiative transport
regime with energy data collected at either single or multiple wavelengths. We
show that when the medium to be probed is non-scattering, explicit
reconstruction schemes can be derived to reconstruct the absorption and the
Gruneisen coefficients. When data at multiple wavelengths are utilized, we can
reconstruct simultaneously the absorption, scattering and Gruneisen
coefficients. We show by numerical simulations that the reconstructions are
stable.Comment: 40 pages, 13 figure
Real-time diffuse optical tomography using reduced-order light propagation models based on a priori anatomical and functional information
This paper proposes a new fast 3D image reconstruction
algorithm for Diffuse Optical Tomography using reduced
order polynomial mappings from the space of optical
tissue parameters into the space of flux measurements at
the detector locations. The polynomial mappings are
constructed through an iterative estimation process
involving structure detection, parameter estimation and
cross-validation using data generated by simulating a
diffusion approximation of the radiative transfer equation
incorporating a priori anatomical and functional
information provided by MR scans and prior psychological
evidence. Numerical simulation studies demonstrate that
reconstructed images are remarkably similar in quality as
those obtained using the standard approach, but obtained at
a fraction of the time
EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments
We review developments, issues and challenges in Electrical Impedance
Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT,
Manchester 2003. We focus on the necessity for three dimensional data
collection and reconstruction, efficient solution of the forward problem and
present and future reconstruction algorithms. We also suggest common pitfalls
or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of
EIT, Manchester, UK, 200
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