1,165 research outputs found
A Framework for Directional and Higher-Order Reconstruction in Photoacoustic Tomography
Photoacoustic tomography is a hybrid imaging technique that combines high
optical tissue contrast with high ultrasound resolution. Direct reconstruction
methods such as filtered backprojection, time reversal and least squares suffer
from curved line artefacts and blurring, especially in case of limited angles
or strong noise. In recent years, there has been great interest in regularised
iterative methods. These methods employ prior knowledge on the image to provide
higher quality reconstructions. However, easy comparisons between regularisers
and their properties are limited, since many tomography implementations heavily
rely on the specific regulariser chosen. To overcome this bottleneck, we
present a modular reconstruction framework for photoacoustic tomography. It
enables easy comparisons between regularisers with different properties, e.g.
nonlinear, higher-order or directional. We solve the underlying minimisation
problem with an efficient first-order primal-dual algorithm. Convergence rates
are optimised by choosing an operator dependent preconditioning strategy. Our
reconstruction methods are tested on challenging 2D synthetic and experimental
data sets. They outperform direct reconstruction approaches for strong noise
levels and limited angle measurements, offering immediate benefits in terms of
acquisition time and quality. This work provides a basic platform for the
investigation of future advanced regularisation methods in photoacoustic
tomography.Comment: submitted to "Physics in Medicine and Biology". Changes from v1 to
v2: regularisation with directional wavelet has been added; new experimental
tests have been include
The Factorization method for three dimensional Electrical Impedance Tomography
The use of the Factorization method for Electrical Impedance Tomography has
been proved to be very promising for applications in the case where one wants
to find inhomogeneous inclusions in a known background. In many situations, the
inspected domain is three dimensional and is made of various materials. In this
case, the main challenge in applying the Factorization method consists in
computing the Neumann Green's function of the background medium. We explain how
we solve this difficulty and demonstrate the capability of the Factorization
method to locate inclusions in realistic inhomogeneous three dimensional
background media from simulated data obtained by solving the so-called complete
electrode model. We also perform a numerical study of the stability of the
Factorization method with respect to various modelling errors.Comment: 16 page
Regularisation methods for imaging from electrical measurements
In Electrical Impedance Tomography the conductivity of an object is estimated from
boundary measurements. An array of electrodes is attached to the surface of the object
and current stimuli are applied via these electrodes. The resulting voltages are measured.
The process of estimating the conductivity as a function of space inside the object from
voltage measurements at the surface is called reconstruction. Mathematically the ElT
reconstruction is a non linear inverse problem, the stable solution of which requires regularisation
methods. Most common regularisation methods impose that the reconstructed image should
be smooth. Such methods confer stability to the reconstruction process, but limit the
capability of describing sharp variations in the sought parameter.
In this thesis two new methods of regularisation are proposed. The first method, Gallssian
anisotropic regularisation, enhances the reconstruction of sharp conductivity changes
occurring at the interface between a contrasting object and the background. As such
changes are step changes, reconstruction with traditional smoothing regularisation techniques
is unsatisfactory. The Gaussian anisotropic filtering works by incorporating prior
structural information. The approximate knowledge of the shapes of contrasts allows us
to relax the smoothness in the direction normal to the expected boundary. The construction
of Gaussian regularisation filters that express such directional properties on the basis
of the structural information is discussed, and the results of numerical experiments are
analysed. The method gives good results when the actual conductivity distribution is in
accordance with the prior information. When the conductivity distribution violates the
prior information the method is still capable of properly locating the regions of contrast.
The second part of the thesis is concerned with regularisation via the total variation
functional. This functional allows the reconstruction of discontinuous parameters. The
properties of the functional are briefly introduced, and an application in inverse problems
in image denoising is shown. As the functional is non-differentiable, numerical difficulties
are encountered in its use. The aim is therefore to propose an efficient numerical implementation
for application in ElT. Several well known optimisation methods arc analysed,
as possible candidates, by theoretical considerations and by numerical experiments. Such
methods are shown to be inefficient. The application of recent optimisation methods
called primal- dual interior point methods is analysed be theoretical considerations and
by numerical experiments, and an efficient and stable algorithm is developed. Numerical
experiments demonstrate the capability of the algorithm in reconstructing sharp conductivity profiles
Template-Based Image Reconstruction from Sparse Tomographic Data
Funder: University of CambridgeAbstract: We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass- or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for mass- and intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially
- …