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

On the Adjoint Operator in Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems

(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods

Imaging is omnipresent in modern society with imaging devices based on a zoo of physical principles, probing a specimen across different wavelengths, energies and time. Recent years have seen a change in the imaging landscape with more and more imaging devices combining that which previously was used separately. Motivated by these hardware developments, an ever increasing set of mathematical ideas is appearing regarding how data from different imaging modalities or channels can be synergistically combined in the image reconstruction process, exploiting structural and/or functional correlations between the multiple images. Here we review these developments, give pointers to important challenges and provide an outlook as to how the field may develop in the forthcoming years. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'

On the inverse problem in optical coherence tomography

We examine the inverse problem of retrieving sample refractive index information in the context of optical coherence tomography. Using two separate approaches, we discuss the limitations of the inverse problem which lead to it being ill-posed, primarily as a consequence of the limited viewing angles available in the reflection geometry. This is first considered from the theoretical point of view of diffraction tomography under a weak scattering approximation. We then investigate the full non-linear inverse problem using a variational approach. This presents another illustration of the non-uniqueness of the solution, and shows that even the non-linear (strongly scattering) scenario suffers a similar fate as the linear problem, with the observable spatial Fourier components of the sample occupying a limited support. Through examples we demonstrate how the solutions to the inverse problem compare when using the variational and diffraction-tomography approaches

A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound

Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic field passing through the skull (e.g., to account for subject-specific dose and targeting variations). As a step towards real-time predictions, in the current work, a fast iterative solver for the heterogeneous Helmholtz equation in 2D is developed using a fully-learned optimizer. The lightweight network architecture is based on a modified UNet that includes a learned hidden state. The network is trained using a physics-based loss function and a set of idealized sound speed distributions with fully unsupervised training (no knowledge of the true solution is required). The learned optimizer shows excellent performance on the test set, and is capable of generalization well outside the training examples, including to much larger computational domains, and more complex source and sound speed distributions, for example, those derived from x-ray computed tomography images of the skull.Comment: 23 pages, 13 figure

Unsupervised Knowledge-Transfer for Learned Image Reconstruction

Deep learning-based image reconstruction approaches have demonstrated impressive empirical performance in many imaging modalities. These approaches generally require a large amount of high-quality training data, which is often not available. To circumvent this issue, we develop a novel unsupervised knowledge-transfer paradigm for learned iterative reconstruction within a Bayesian framework. The proposed approach learns an iterative reconstruction network in two phases. The first phase trains a reconstruction network with a set of ordered pairs comprising of ground truth images and measurement data. The second phase fine-tunes the pretrained network to the measurement data without supervision. Furthermore, the framework delivers uncertainty information over the reconstructed image. We present extensive experimental results on low-dose and sparse-view computed tomography, showing that the proposed framework significantly improves reconstruction quality not only visually, but also quantitatively in terms of PSNR and SSIM, and is competitive with several state-of-the-art supervised and unsupervised reconstruction techniques

A spread spectrum approach to time-domain near-infrared diffuse optical imaging using inexpensive optical transceiver modules

We introduce a compact time-domain system for near-infrared spectroscopy using a spread spectrum technique. The proof-of-concept single channel instrument utilises a low-cost commercially available optical transceiver module as a light source, controlled by a Kintex 7 field programmable gate array (FPGA). The FPGA modulates the optical transceiver with maximum-length sequences at line rates up to 10Gb/s, allowing us to achieve an instrument response function with full width at half maximum under 600ps. The instrument is characterised through a set of detailed phantom measurements as well as proof-of-concept in vivo measurements, demonstrating performance comparable with conventional pulsed time-domain near-infrared spectroscopy systems

A matrix-free algorithm for multiple wavelength fluorescence tomography

In the recent years, there has been an increase in applications of non-contact diffusion optical tomography. Especially when the objective is the recovery of fluorescence targets. The non-contact acquisition systems with the use of a CCD-camera produce much denser sampled boundary data sets than fibre-based systems. When model-based reconstruction methods are used, that rely on the inversion of a derivative operator, the large number of measurements poses a challenge since the explicit formulation and storage of the Jacobian matrix could be in general not feasible. This problem is aggravated further in applications, where measurements at multiple wavelengths are used. We present a matrix-free model-based reconstruction method, that addresses the problems of large data sets and reduces the computational cost and memory requirements for the reconstruction. The idea behind the matrix-free method is that information about the Jacobian matrix could be available through matrix times vector products so that the creation and storage of big matrices can be avoided. We tested the method for multiple wavelength fluorescence tomography with simulated and experimental data from phantom experiments, and we found substantial benefits in computational times and memory requirements. (C) 2009 Optical Society of Americ

Clinical impact of respiratory motion correction in simultaneous PET/MR, using a joint PET/MR predictive motion model

In Positron Emission Tomography (PET) imaging, patient motion due to respiration can lead to artefacts and blurring, in addition to quantification errors. The integration of PET imaging with Magnetic Resonance (MR) imaging in PET/MR scanners provides spatially aligned complementary clinical information, and allows the use of high spatial resolution and high contrast MR images to monitor and correct motion-corrupted PET data. We validate our PET respiratory motion correction methodology based on a joint PET-MR motion model, on a patient cohort, showing it can improve lesion detectability and quantitation, and reduce image artefacts. Methods: We apply our motion correction methodology on 42 clinical PET-MR patient datasets, using multiple tracers and multiple organ locations, containing 162 PET-avid lesions. Quantitative changes are calculated using Standardised Uptake Value (SUV) changes in avid lesions. Lesion detectability changes are explored with a study where two radiologists identify lesions or \u27hot spots\u27, providing confidence levels, in uncorrected and motion-corrected images. Results: Mean increases of 12.4% for SUV_peak and 17.6% for SUV_max following motion correction were found. In the detectability study, an increase in confidence scores for detecting avid lesions is shown, with a mean score of 2.67 rising to 3.01 (out of 4) after motion correction, and a detection rate of 74% rising to 84%. Of 162 confirmed lesions, 49 lesions showed an increase in all three metrics SUV_peak, SUV_max and combined reader confidence scores, whilst only two lesions showed a decrease. We also present a number of clinical case studies, demonstrating the effect respiratory motion correction of PET data can have on patient management, with increased numbers of lesions detected, improved lesion sharpness and localisation, as well as reduced attenuation-based artefacts. Conclusion: We demonstrate significant improvements in quantification and detection of PET-avid lesions, with specific case study examples showing where motion correction has the potential to have an effect on patient diagnosis or care