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

The cushion region and dayside magnetodisc structure at Saturn

A sustained dipolar magnetic field between the current sheet outer edge and the magnetopause, known as a cushion region, has yet to be observed at Saturn. Whilst some signatures of reconnection occurring in the dayside magnetodisc have been identified, the presence of this large-scale structure has not been seen. Using the complete Cassini magnetometer data, the first evidence of a cushion region forming at Saturn is shown. Only five potential examples of a sustained cushion are found, revealing this phenomenon to be rare. This feature more commonly occurs at dusk compared to dawn, where it is found at Jupiter. It is suggested that due to greater heating and expansion of the field through the afternoon sector the disc is more unstable in this region. We show that magnetodisc breakdown is more likely to occur within the magnetosphere of Jupiter compared to Saturn

Radiance Monte-Carlo for application of the radiative transport equation in the inverse problem of diffuse optical tomography

We introduce a new Monte-Carlo technique to estimate the radiance distribution in a medium according to the radiative transport equation (RTE). We demonstrate how to form gradients of the forward model, and thus how to employ this technique as part of the inverse problem in Diffuse Optical Tomography (DOT). Use of the RTE over the more typical application of the diffusion approximation permits accurate modelling in the case of short source-detector separation and regions of low scattering, in addition to providing time-domain information without extra computational effort over continuous-wave solutions

Forward and Adjoint Radiance Monte Carlo Models for Quantitative Photoacoustic Imaging

In quantitative photoacoustic imaging, the aim is to recover physiologically relevant tissue parameters such as chromophore concentrations or oxygen saturation. Obtaining accurate estimates is challenging due to the non-linear relationship between the concentrations and the photoacoustic images. Nonlinear least squares inversions designed to tackle this problem require a model of light transport, the most accurate of which is the radiative transfer equation. This paper presents a highly scalable Monte Carlo model of light transport that computes the radiance in 2D using a Fourier basis to discretise in angle. The model was validated against a 2D finite element model of the radiative transfer equation, and was used to compute gradients of an error functional with respect to the absorption and scattering coefficient. It was found that adjoint-based gradient calculations were much more robust to inherent Monte Carlo noise than a finite difference approach. Furthermore, the Fourier angular discretisation allowed very efficient gradient calculations as sums of Fourier coefficients. These advantages, along with the high parallelisability of Monte Carlo models, makes this approach an attractive candidate as a light model for quantitative inversion in photoacoustic imaging

Uncertainty quantification in medical image synthesis

Machine learning approaches to medical image synthesis have shown outstanding performance, but often do not convey uncertainty information. In this chapter, we survey uncertainty quantification methods in medical image synthesis and advocate the use of uncertainty for improving clinicians’ trust in machine learning solutions. First, we describe basic concepts in uncertainty quantification and discuss its potential benefits in downstream applications. We then review computational strategies that facilitate inference, and identify the main technical and clinical challenges. We provide a first comprehensive review to inform how to quantify, communicate and use uncertainty in medical synthesis applications

Validation of a finite-element solution for electrical impedance tomography in an anisotropic medium

Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, implementations have neglected anisotropy even though human tissues such as bone, muscle and brain white matter are markedly anisotropic. We present a numerical solution using the finite-element method that has been modified for modelling anisotropic conductive media. It was validated in an anisotropic domain against an analytical solution in an isotropic medium after the isotropic domain was diffeomorphically transformed into an anisotropic one. Convergence of the finite element to the analytical solution was verified by showing that the finite-element error norm decreased linearly related to the finite-element size, as the mesh density increased, for the simplified case of Laplace's equation in a cubic domain with a Dirichlet boundary condition

Inversion formulas for the broken-ray Radon transform

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the filtered backprojection formula of the conventional Radon transform. The advantages of the broken ray transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium simultaneously and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem

Multiple Projection Optical Diffusion Tomography with Plane Wave Illumination

We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the slab around the sample. The advantage of the proposed method is that the measured data can be much more easily fitted into the dynamic range of most commonly used detectors. At the same time, multiple projections improve image quality by mutually interchanging the depth and transverse directions, and the scanned (detection) and integrated (illumination) surfaces. Inversion methods are derived for image reconstructions with extremely large data sets. Numerical simulations are performed for fixed and rotated slabs

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

Iterative PET Image Reconstruction using Adaptive Adjustment of Subset Size and Random Subset Sampling

Statistical PET image reconstruction methods are often accelerated by the use of a subset of available projections at each iteration. It is known that many subset algorithms, such as ordered subset expectation maximisation, will not converge to a single solution but to a limit cycle. Reconstruction methods exist to relax the update step sizes of subset algorithms to obtain convergence, however, this introduces additional parameters that may result in extended reconstruction times. Another approach is to gradually decrease the number of subsets to reduce the effect of the limit cycle at later iterations, but the optimal iteration numbers for these reductions may be data dependent. We propose an automatic method to increase subset sizes so a reconstruction can take advantage of the acceleration provided by small subset sizes during early iterations, while at later iterations reducing the effects of the limit cycle behaviour providing estimates closer to the maximum a posteriori solution. At each iteration, two image updates are computed from a common estimate using two disjoint subsets. The divergence of the two update vectors is measured and, if too great, subset sizes are increased in future iterations. We show results for both sinogram and list mode data using various subset selection methodologies