The D-bar Method for Diffuse Optical Tomography: a computational study

The D-bar method at negative energy is numerically implemented. Using the method we are able to numerically reconstruct potentials and investigate exceptional points at negative energy. Subsequently, applying the method to Diffusive Optical Tomography, a new way of reconstructing the diffusion coefficient from the associated Complex Geometrics Optics solution is suggested and numerically validated

Towards a d-bar reconstruction method for three-dimensional EIT

Abstract. Three-dimensional electrical impedance tomography (EIT) is considered. Both uniqueness proofs and theoretical reconstruction algorithms available for this problem rely on the use of exponentially growing solutions to the governing conductivity equation. The study of those solutions is continued here. It is shown that exponentially growing solutions exist for low complex frequencies without imposing any regularity assumption on the conductivity. Further, a reconstruction method for conductivities close to a constant is given. In this method the complex frequency is taken to zero instead of infinity. Since this approach involves only moderately oscillatory boundary data, it enables a new class of three-dimensional EIT algorithms, free from the usual high frequency instabilities. 1

The D-Bar Method for Diffuse Optical Tomography : A Computational Study

The D-bar method at negative energy is numerically implemented. Using the method, we are able to numerically reconstruct potentials and investigate exceptional points at negative energy. Subsequently, applying the method to diffuse optical tomography, a new way of reconstructing the diffusion coefficient from the associated Complex Geometrics Optics solution is suggested and numerically validated.Peer reviewe

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.Comment: This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/28/9/09500

Imaging of moisture content in wood using electrical capacitance tomography

http://shop.tuverlag.at/de/the-world-conference-on-timber-engineeringThe current study investigates whether an electrical imaging modality, electrical capacitance tomography (ECT), could provide information on the moisture content in wood. In ECT, a set of electrodes are placed around the surface of the object, and based on electrical capacitance measurements from the surface, the spatial distribution of the electrical permittivity inside the object is reconstructed. In this experimental study, water is infiltrated in a wood sample for 7 days, and ECT measurements are sequentially collected during the absorption of water. The reconstructed ECT images show a constant increase of electrical permittivity in the location of water absorption. The results support the feasibility of ECT for imaging the water content in wood.Peer reviewe

Anatomical atlas of the upper part of the human head for electroencephalography and bioimpedance applications

Objective. The objective of this work is to develop a 4D (3D+T) statistical anatomical atlas of the electrical properties of the upper part of the human head for cerebral electrophysiology and bioimpedance applications. Approach. The atlas was constructed based on 3D magnetic resonance images (MRI) of 107 human individuals and comprises the electrical properties of the main internal structures and can be adjusted for specific electrical frequencies. T1w+T2w MRI images were used to segment the main structures of the head while angiography MRI was used to segment the main arteries. The proposed atlas also comprises a time-varying model of arterial brain circulation, based on the solution of the Navier-Stokes equation in the main arteries and their vascular territories. Main results. High-resolution, multi-frequency and time-varying anatomical atlases of resistivity, conductivity and relative permittivity were created and evaluated using a forward problem solver for EIT. The atlas was successfully used to simulate electrical impedance tomography measurements indicating the necessity of signal-to-noise between 100 and 125 dB to identify vascular changes due to the cardiac cycle, corroborating previous studies. The source code of the atlas and solver are freely available to download. Significance. Volume conductor problems in cerebral electrophysiology and bioimpedance do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its electrical properties for solving the associated PDEs numerically. Ideally, the model should be made with patient-specific information. In clinical practice, this is not always the case and an average head model is often used. Also, the electrical properties of the tissues might not be completely known due to natural variability. Anatomical atlases are important tools for in silico studies on cerebral circulation and electrophysiology that require statistically consistent data, e.g. machine learning, sensitivity analyses, and as a benchmark to test inverse problem solvers.Peer reviewe

Deep Neural Networks for Inverse Problems with Pseudodifferential Operators: An Application to Limited-Angle Tomography

We propose a novel convolutional neural network (CNN), called \Psi DONet, designed for learning pseudodifferential operators (\Psi DOs) in the context of linear inverse problems. Our starting point is the iterative soft thresholding algorithm (ISTA), a well-known algorithm to solve sparsity-promoting minimization problems. We show that, under rather general assumptions on the forward operator, the unfolded iterations of ISTA can be interpreted as the successive layers of a CNN, which in turn provides fairly general network architectures that, for a specific choice of the parameters involved, allow us to reproduce ISTA, or a perturbation of ISTA for which we can bound the coefficients of the filters. Our case study is the limited-angle X-ray transform and its application to limited-angle computed tomography (LA-CT). In particular, we prove that, in the case of LA-CT, the operations of upscaling, downscaling, and convolution, which characterize our \Psi DONet and most deep learning schemes, can be exactly determined by combining the convolutional nature of the limited-angle Xray transform and basic properties defining an orthogonal wavelet system. We test two different implementations of \Psi DONet on simulated data from limited-angle geometry, generated from the ellipse data set. Both implementations provide equally good and noteworthy preliminary results, showing the potential of the approach we propose and paving the way to applying the same idea to other convolutional operators which are \Psi DOs or Fourier integral operators

Iterative and discrete reconstruction in the evaluation of the rabbit model of osteoarthritis

Micro-computed tomography (µCT) is a standard method for bone morphometric evaluation. However, the scan time can be long and the radiation dose during the scan may have adverse effects on test subjects, therefore both of them should be minimized. This could be achieved by applying iterative reconstruction (IR) on sparse projection data, as IR is capable of producing reconstructions of sufficient image quality with less projection data than the traditional algorithm requires. In this work, the performance of three IR algorithms was assessed for quantitative bone imaging from low-resolution data in the evaluation of the rabbit model of osteoarthritis. Subchondral bone images were reconstructed with a conjugate gradient least squares algorithm, a total variation regularization scheme, and a discrete algebraic reconstruction technique to obtain quantitative bone morphometry, and the results obtained in this manner were compared with those obtained from the reference reconstruction. Our approaches were sufficient to identify changes in bone structure in early osteoarthritis, and these changes were preserved even when minimal data were provided for the reconstruction. Thus, our results suggest that IR algorithms give reliable performance with sparse projection data, thereby recommending them for use in µCT studies where time and radiation exposure are preferably minimized. © 2018, The Author(s).Peer reviewe