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Ben Cox

Publications and source records attributed to Ben Cox.

At least 19 recordsLinked to original sources
arXiv2025

Reconstructing initial pressure and speed of sound distributions simultaneously in photoacoustic tomography

Image reconstruction in photoacoustic tomography relies on an accurate knowledge of the speed of sound in the target. However, the speed of sound distribution is not generally known, which may result in artefacts in the reconstructed distribution of initial pressure. Therefore, reconstructing the speed of sound simultaneously with the initial pressure would be valuable for accurate imaging in photoacoustic tomography. Furthermore, the speed of sound distribution could provide additional valuable information about the imaged target. In this work, simultaneous reconstruction of initial pressure and speed of sound in photoacoustic tomography is studied. This inverse problem is known to be highly ill-posed. To overcome this, we study an approach where the ill-posedness is alleviated by utilising multiple photoacoustic data sets that are generated by different initial pressure distributions within the same imaged target. Then, these initial pressure distributions are reconstructed simultaneously with the speed of sound distribution. A methodology for solving this minimisation problem is formulated using a gradient-based iterative approach equipped with bound constraints and a multigrid approach. The methodology was evaluated with numerical simulations. Different approaches for generating multiple initial pressure distributions and their effect on the solution of the image reconstruction problem were studied. The results show that initial pressure and speed of sound can be simultaneously reconstructed from photoacoustic data. Furthermore, utilising multiple initial pressure distributions improves the reconstructions such that the locations of initial pressure and speed of sound inhomogeneities can be better distinguished and image artifacts are reduced.

physics.med-ph↗
arXiv2024

Existence of solutions to k-Wave models of nonlinear ultrasound propagation in biological tissue

We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solved for the acoustic particle velocity, mass density, and acoustic pressure and involve a fractional absorption operator. We first consider a system that incorporates additional viscosity in the equation for momentum conservation. By constructing a Galerkin approximation procedure, we prove the local existence of its solutions. In view of inverse problems arising from imaging tasks, the theory allows for the variable background mass density, speed of sound, and the nonlinearity parameter in the systems. Secondly, under stronger conditions on the data, we take the vanishing viscosity limit of the problem, thereby rigorously establishing the existence of solutions for the limiting system as well.

math.AP↗
arXiv2022

Phase-insensitive versus phase-sensitive ultrasound absorption tomography in the frequency domain

The sensitivity of phase-sensitive detectors, such as piezoelectric detectors, becomes increasingly directional as the detector element size increases. In contrast, pyroelectric sensors, which are phase-insensitive, retain their omni-directionality even for large element sizes, although they have significantly poorer temporal resolution. This study uses numerical models to examine whether phase-insensitive detectors can be used advantageously in ultrasound tomography, specifically absorption tomography, when the number of detectors is sparse. We present measurement models for phase-sensitive and phase-insensitive sensors and compare the quality of the absorption reconstructions between these sensor types based on image contrast metrics. We perform the inversion using synthetic data with a Jacobian-based linearised matrix inversion approach.

math.NA↗
arXiv2021

Ray-based inversion accounting for scattering for biomedical ultrasound computed tomography

An efficient and accurate image reconstruction algorithm for ultrasound tomography (UST) is described and demonstrated, which can recover accurate sound speed distribution from acoustic time series measurements made in soft tissue. The approach is based on a second-order iterative minimisation of the difference between the measurements and a model based on a ray-approximation to the heterogeneous Green's function. It overcomes the computational burden of full-wave solvers while avoiding the drawbacks of time-of-flight methods. Through the use of a second-order iterative minimisation scheme, applied stepwise from low to high frequencies, the effects of scattering are incorporated into the inversion.

math.NA↗
arXiv2020

Deep Learning in Photoacoustic Tomography: Current approaches and future directions

Biomedical photoacoustic tomography, which can provide high resolution 3D soft tissue images based on the optical absorption, has advanced to the stage at which translation from the laboratory to clinical settings is becoming possible. The need for rapid image formation and the practical restrictions on data acquisition that arise from the constraints of a clinical workflow are presenting new image reconstruction challenges. There are many classical approaches to image reconstruction, but ameliorating the effects of incomplete or imperfect data through the incorporation of accurate priors is challenging and leads to slow algorithms. Recently, the application of Deep Learning, or deep neural networks, to this problem has received a great deal of attention. This paper reviews the literature on learned image reconstruction, summarising the current trends, and explains how these new approaches fit within, and to some extent have arisen from, a framework that encompasses classical reconstruction methods. In particular, it shows how these new techniques can be understood from a Bayesian perspective, providing useful insights. The paper also provides a concise tutorial demonstration of three prototypical approaches to learned image reconstruction. The code and data sets for these demonstrations are available to researchers. It is anticipated that it is in in vivo applications - where data may be sparse, fast imaging critical and priors difficult to construct by hand - that Deep Learning will have the most impact. With this in mind, the paper concludes with some indications of possible future research directions.

eess.IV↗
arXiv2020

Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast

Ultrasound Tomography has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional ultrasound tomography, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray ultrasound tomography in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and three robust, accurate, and efficient ray-linking algorithms are formulated and demonstrated. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions.

physics.comp-ph↗
arXiv2020

Towards accurate quantitative photoacoustic imaging: learning vascular blood oxygen saturation in 3D

Significance: 2D fully convolutional neural networks have been shown capable of producing maps of sO$_2$ from 2D simulated images of simple tissue models. However, their potential to produce accurate estimates in vivo is uncertain as they are limited by the 2D nature of the training data when the problem is inherently 3D, and they have not been tested with realistic images. Aim: To demonstrate the capability of deep neural networks to process whole 3D images and output 3D maps of vascular sO$_2$ from realistic tissue models/images. Approach: Two separate fully convolutional neural networks were trained to produce 3D maps of vascular blood oxygen saturation and vessel positions from multiwavelength simulated images of tissue models. Results: The mean of the absolute difference between the true mean vessel sO$_2$ and the network output for 40 examples was 4.4% and the standard deviation was 4.5%. Conclusions: 3D fully convolutional networks were shown capable of producing accurate sO$_2$ maps using the full extent of spatial information contained within 3D images generated under conditions mimicking real imaging scenarios. This work demonstrates that networks can cope with some of the confounding effects present in real images such as limited-view artefacts, and have the potential to produce accurate estimates in vivo.

physics.med-ph↗
arXiv2018

Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category $\mathcal O^q_{\text{red,im}}$

Recently we defined imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$- modules in category $\mathcal O^q_{\text{red,im}}$ and showed the existence of such bases for reduced quantized imaginary Verma modules for $U_q(\widehat{\mathfrak{sl}(2)})$. In this paper we show the existence of imaginary crystal basis for any object in the category $\mathcal O^q_{\text{red,im}}$.

math.RT↗
arXiv2018

On the module structure of the center of hyperelliptic Krichever-Novikov algebras II

Let $R := R_{2}(p)=\mathbb{C}[t^{\pm 1}, u : u^2 = t(t-\alpha_1)\cdots (t-\alpha_{2n})] $ be the coordinate ring of a nonsingular hyperelliptic curve and let $\mathfrak{g}\otimes R$ be the corresponding current Lie algebra. \color{black} Here $\mathfrak g$ is a finite dimensional simple Lie algebra defined over $\mathbb C$ and \begin{equation*} p(t)= t(t-\alpha_1)\cdots (t-\alpha_{2n})=\sum_{k=1}^{2n+1}a_kt^k. \end{equation*} In earlier work, Cox and Im gave a generator and relations description of the universal central extension of $\mathfrak{g}\otimes R$ in terms of certain families of polynomials $P_{k,i}$ and $Q_{k,i}$ and they described how the center $\Omega_R/dR$ of this universal central extension decomposes into a direct sum of irreducible representations when the automorphism group was the cyclic group $C_{2k}$ or the dihedral group $D_{2k}$. We give examples of $2n$-tuples $(\alpha_1,\dots,\alpha_{2n})$, which are the automorphism groups $\mathbb G_n=\text{Dic}_{n}$, $\mathbb U_n\cong D_n$ ($n$ odd), or $\mathbb U_n$ ($n$ even) of the hyperelliptic curves \begin{equation} S=\mathbb{C}[t, u: u^2 = t(t-\alpha_1)\cdots (t-\alpha_{2n})] \end{equation} given in [CGLZ17]. In the work below, we describe this decomposition when the automorphism group is $\mathbb U_n=D_n$, where $n$ is odd.

math.RT↗
arXiv2018

Approximate k-space models and Deep Learning for fast photoacoustic reconstruction

We present a framework for accelerated iterative reconstructions using a fast and approximate forward model that is based on k-space methods for photoacoustic tomography. The approximate model introduces aliasing artefacts in the gradient information for the iterative reconstruction, but these artefacts are highly structured and we can train a CNN that can use the approximate information to perform an iterative reconstruction. We show feasibility of the method for human in-vivo measurements in a limited-view geometry. The proposed method is able to produce superior results to total variation reconstructions with a speed-up of 32 times.

cs.CV↗
arXiv2018

Categorification of Verma modules and indecomposable projective modules in the category $\mathcal I_{\mathfrak{g}}(\mathfrak{sl}_2)$ for $\mathfrak{sl}_2$

We categorify Verma and indecomposable projective modules in the category $\mathcal I_{\mathfrak{g}}(\mathfrak{sl}_2)$ for $\mathfrak{sl}_2$ using a tensor product decomposition theorem of T. J. Enright and work of J. Chuang and R. Rouquier, A. Licata and A. Savage (Hecke algebras, finite general linear groups, and Heisenberg categorification) and M. Khovanov (Heisenberg algebra and a graphical calculus).

math.RT↗
arXiv2018

Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion Estimation

A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: images with good spatial resolution and contrast can be obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning systems if sparsity-constrained image reconstruction techniques such as total variation regularization are used. Now, we show how a further increase of image quality can be achieved for imaging dynamic processes in living tissue (4D PAT). The key idea is to exploit the additional temporal redundancy of the data by coupling the previously used spatial image reconstruction models with sparsity-constrained motion estimation models. While simulated data from a two-dimensional numerical phantom will be used to illustrate the main properties of this recently developed joint-image-reconstruction-and-motion-estimation framework, measured data from a dynamic experimental phantom will also be used to demonstrate their potential for challenging, large-scale, real-world, three-dimensional scenarios. The latter only becomes feasible if a carefully designed combination of tailored optimization schemes is employed, which we describe and examine in more detail.

math.NA↗
arXiv2017

Model based learning for accelerated, limited-view 3D photoacoustic tomography

Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide high resolution 3D images from restricted photoacoustic measurements. The network is designed to represent an iterative scheme and incorporates gradient information of the data fit to compensate for limited view artefacts. Due to the high complexity of the photoacoustic forward operator, we separate training and computation of the gradient information. A suitable prior for the desired image structures is learned as part of the training. The resulting network is trained and tested on a set of segmented vessels from lung CT scans and then applied to in-vivo photoacoustic measurement data.

cs.CV↗
arXiv2017

On the module structure of the center of hyperelliptic Krichever-Novikov algebras

We consider the coordinate ring of a hyperelliptic curve and let $\mathfrak{g}\otimes R$ be the corresponding current Lie algebra where $\mathfrak g$ is a finite dimensional simple Lie algebra defined over $\mathbb C$. We give a generator and relations description of the universal central extension of $\mathfrak{g}\otimes R$ in terms of certain families of polynomials $P_{k,i}$ and $Q_{k,i}$ and describe how the center $\Omega_R/dR$ decomposes into a direct sum of irreducible representations when the automorphism group is $C_{2k}$ or $D_{2k}$.

math.RT↗
arXiv2016

Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance

Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A 2D radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance in heterogeneous media. A gradient-based optimisation scheme is then used to recover 2D absorption and scattering coefficients distributions from simulated photoacoustic measurements. It is shown that the functional gradients, which are a challenge to compute efficiently using MC models, can be calculated directly from the coefficients of the harmonic angular basis used in the forward and adjoint models. This work establishes a framework for transport-based quantitative photoacoustic tomography that can fully exploit emerging highly parallel computing architectures.

physics.med-ph↗
arXiv2016

Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing

Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. A particular example is the planar Fabry-Perot (FP) scanner, which yields high-resolution images but takes several minutes to sequentially map the photoacoustic field on the sensor plane, point-by-point. However, as the spatio-temporal complexity of many absorbing tissue structures is rather low, the data recorded in such a conventional, regularly sampled fashion is often highly redundant. We demonstrate that combining variational image reconstruction methods using spatial sparsity constraints with the development of novel PAT acquisition systems capable of sub-sampling the acoustic wave field can dramatically increase the acquisition speed while maintaining a good spatial resolution: First, we describe and model two general spatial sub-sampling schemes. Then, we discuss how to implement them using the FP scanner and demonstrate the potential of these novel compressed sensing PAT devices through simulated data from a realistic numerical phantom and through measured data from a dynamic experimental phantom as well as from in-vivo experiments. Our results show that images with good spatial resolution and contrast can be obtained from highly sub-sampled PAT data if variational image reconstruction methods that describe the tissues structures with suitable sparsity-constraints are used. In particular, we examine the use of total variation regularization enhanced by Bregman iterations. These novel reconstruction strategies offer new opportunities to dramatically increase the acquisition speed of PAT scanners that employ point-by-point sequential scanning as well as reducing the channel count of parallelized schemes that use detector arrays.

math.NA↗