9,335 research outputs found
Linearized Reconstruction for Diffuse Optical Spectroscopic Imaging
In this paper, we present a novel reconstruction method for diffuse optical
spectroscopic imaging with a commonly used tissue model of optical absorption
and scattering. It is based on linearization and group sparsity, which allows
recovering the diffusion coefficient and absorption coefficient simultaneously,
provided that their spectral profiles are incoherent and a sufficient number of
wavelengths are judiciously taken for the measurements. We also discuss the
reconstruction for imperfectly known boundary and show that with the
multi-wavelength data, the method can reduce the influence of modelling errors
and still recover the absorption coefficient. Extensive numerical experiments
are presented to support our analysis.Comment: 18 pages, 7 figure
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
Gradient-based quantitative image reconstruction in ultrasound-modulated optical tomography: first harmonic measurement type in a linearised diffusion formulation
Ultrasound-modulated optical tomography is an emerging biomedical imaging
modality which uses the spatially localised acoustically-driven modulation of
coherent light as a probe of the structure and optical properties of biological
tissues. In this work we begin by providing an overview of forward modelling
methods, before deriving a linearised diffusion-style model which calculates
the first-harmonic modulated flux measured on the boundary of a given domain.
We derive and examine the correlation measurement density functions of the
model which describe the sensitivity of the modality to perturbations in the
optical parameters of interest. Finally, we employ said functions in the
development of an adjoint-assisted gradient based image reconstruction method,
which ameliorates the computational burden and memory requirements of a
traditional Newton-based optimisation approach. We validate our work by
performing reconstructions of optical absorption and scattering in two- and
three-dimensions using simulated measurements with 1% proportional Gaussian
noise, and demonstrate the successful recovery of the parameters to within
+/-5% of their true values when the resolution of the ultrasound raster probing
the domain is sufficient to delineate perturbing inclusions.Comment: 12 pages, 6 figure
Experimental demonstration of an analytic method for image reconstruction in optical tomography with large data sets
We report the first experimental test of an analytic image reconstruction
algorithm for optical tomography with large data sets. Using a continuous-wave
optical tomography system with 10^8 source-detector pairs, we demonstrate the
reconstruction of an absorption image of a phantom consisting of a
highly-scattering medium with absorbing inhomogeneities.Comment: 3 pages, 3 figure
Fast and efficient image reconstruction for high density diffuse optical imaging of the human brain
Real-time imaging of human brain has become an important technique within neuroimaging. In this study, a fast and efficient sensitivity map generation based on Finite Element Models (FEM) is developed which utilises a reduced sensitivitys matrix taking advantage of sparsity and parallelisation processes. Time and memory efficiency of these processes are evaluated and compared with conventional method showing that for a range of mesh densities from 50000 to 320000 nodes, the required memory is reduced over tenfold and computational time fourfold allowing for near real-time image recovery
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