arXiv subjects

Ben T. Cox

Publications and source records attributed to Ben T. Cox.

At least 19 recordsLinked to original sources

arXiv2025

Learning Greens Operators through Hierarchical Neural Networks Inspired by the Fast Multipole Method

The Fast Multipole Method (FMM) is an efficient numerical algorithm for computation of long-ranged forces in $N$-body problems within gravitational and electrostatic fields. This method utilizes multipole expansions of the Green's function inherent to the underlying dynamical systems. Despite its widespread application in physics and engineering, the integration of FMM with modern machine learning architectures remains underexplored. In this work, we propose a novel neural network architecture, the Neural FMM, that integrates the information flow of the FMM into a hierarchical machine learning framework for learning the Green's operator of an Elliptic PDE. Our Neural FMM architecture leverages a hierarchical computation flow of the FMM method to split up the local and far-field interactions and efficiently learn their respective representations.

cs.LG↗

arXiv2025

Digital twins enable full-reference quality assessment of photoacoustic image reconstructions

Quantitative comparison of the quality of photoacoustic image reconstruction algorithms remains a major challenge. No-reference image quality measures are often inadequate, but full-reference measures require access to an ideal reference image. While the ground truth is known in simulations, it is unknown in vivo, or in phantom studies, as the reference depends on both the phantom properties and the imaging system. We tackle this problem by using numerical digital twins of tissue-mimicking phantoms and the imaging system to perform a quantitative calibration to reduce the simulation gap. The contributions of this paper are two-fold: First, we use this digital-twin framework to compare multiple state-of-the-art reconstruction algorithms. Second, among these is a Fourier transform-based reconstruction algorithm for circular detection geometries, which we test on experimental data for the first time. Our results demonstrate the usefulness of digital phantom twins by enabling assessment of the accuracy of the numerical forward model and enabling comparison of image reconstruction schemes with full-reference image quality assessment. We show that the Fourier transform-based algorithm yields results comparable to those of iterative time reversal, but at a lower computational cost. All data and code are publicly available on Zenodo: https://doi.org/10.5281/zenodo.15388429.

physics.med-ph↗

arXiv2025

Artifacts in Photoacoustic Imaging: Origins and Mitigations

Photoacoustic imaging (PAI) is rapidly moving from the laboratory to the clinic, increasing the need to understand confounders which might adversely affect patient care. Over the past five years, landmark studies have shown the clinical utility of PAI, leading to regulatory approval of several devices. In this article, we describe the various causes of artifacts in PAI, providing schematic overviews and practical examples, simulated as well as experimental. This work serves two purposes: (1) educating clinical users to identify artifacts, understand their causes, and assess whether their impact, and (2) providing a reference of the limitations of current systems for those working to improve them. We explain how two aspects of PAI systems lead to artifacts: their inability to measure complete data sets, and embedded assumptions during reconstruction. We describe the physics underlying PAI, and propose a classification of the artifacts. The paper concludes by discussing possible advanced mitigation strategies.

physics.med-ph↗

arXiv2023

Enhancing synthetic training data for quantitative photoacoustic tomography with generative deep learning

Multiwavelength photoacoustic images encode information about a tissue's optical absorption distribution. This can be used to estimate its blood oxygen saturation distribution (sO2), an important physiological indicator of tissue health and pathology. However the wavelength dependence of the light fluence distribution complicates the recovery of accurate estimates, in particular, preventing the use of a straightforward spectroscopic inversion. Deep learning approaches have been shown effective at producing accurate estimates of sO2 from simulated data. Though, the translation of generic supervised learning approaches to real tissues is prevented by the lack of real `paired' training data (multiwavelength PA images of in vivo tissues with their corresponding sO2 distributions). Here, we discuss i) why networks trained on images simulated using conventional means are unlikely to generalise their performance on real tissues, and ii) the prospects of using two generative adversarial network based strategies to improve the generalisability of sO2-estimating networks trained on synthetic data: a) CycleGAN-driven unsupervised domain adaptation of conventionally simulated images, and b) the generation of paired training data using AmbientGANs.

physics.med-ph↗

arXiv2023

Physics-Based Acoustic Holograms

Advances in additive manufacturing have enabled the realisation of inexpensive, scalable, diffractive acoustic lenses that can be used to generate complex acoustic fields via phase and/or amplitude modulation. However, the design of these holograms relies on a thin-element approximation adapted from optics which can severely limit the fidelity of the realised acoustic field. Here, we introduce physics-based acoustic holograms with a complex internal structure. The structures are designed using a differentiable acoustic model with manufacturing constraints via optimisation of the acoustic property distribution within the hologram. The holograms can be fabricated simply and inexpensively using contemporary 3D printers. Experimental measurements demonstrate a significant improvement compared to conventional thin-element holograms.

cs.SD↗

arXiv2023

open-UST: An Open-Source Ultrasound Tomography Transducer Array System

Fast imaging methods are needed to promote widespread clinical adoption of Ultrasound Tomography (UST), and more widely available UST hardware could support the experimental validation of new measurement configurations. In this work, an open-source 256-element transducer ring array was developed (morganjroberts.github.io/open-UST) and manufactured using rapid prototyping, for only £2k. Novel manufacturing techniques were used, resulting in a 1.17$^{\circ}$ mean beam axis skew angle, a 104 $μ$m mean element position error, and a $\pm$13.6 $μ$m deviation in matching layer thickness. The nominal acoustic performance was measured using hydrophone scans and watershot data, and the 61.2 dB SNR, 55.4$^{\circ}$ opening angle, 16.3 mm beamwidth and 54% transmit-receive bandwidth (-12 dB), were found to be similar to existing systems, and compatible with full waveform inversion reconstruction methods. The inter-element variation in acoustic performance was typically <10% without using normalisation, meaning that the elements can be modelled identically during image reconstruction, removing the need for individual source definitions based on hydrophone measurements. Finally, data from a phantom experiment was successfully reconstructed. These results demonstrate that the open-UST system is accessible for users, and suitable for UST imaging research.

physics.med-ph↗

arXiv2022

A Learned Born Series for Highly-Scattering Media

A new method for solving the wave equation is presented, called the learned Born series (LBS), which is derived from a convergent Born Series but its components are found through training. The LBS is shown to be significantly more accurate than the convergent Born series for the same number of iterations, in the presence of high contrast scatterers, while maintaining a comparable computational complexity. The LBS is able to generate a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations.

physics.comp-ph↗

arXiv2022

Binary Volume Acoustic Holograms

In recent years high-resolution 3D printing has enabled a diverse range of new, low-cost, methods for ultrasonic wave-front shaping. Acoustic holograms, particularly, allow for the generation of arbitrary, diffraction limited, acoustic fields at MHz frequencies from single element transducers. These are phase plates that function as direct acoustic analogues to thin optical holograms. In this work it is shown that, by using multiple polymer 3D printing, acoustic analogues to 'thick' or volume optical holograms can also be generated. First, an analytic approach for designing a volume hologram that diffracts a set of input fields onto a desired set of output fields is briefly summarised. Next, a greedy optimisation approach based on random downhill binary search able to account for the constraints imposed by the chosen fabrication method is introduced. Finally, an experimental test-case designed to diffract the field generated by a 2.54 cm, planar, PZT transducer onto 8 distinct patterns dependent on the direction of the incident field is used to validate the approach and the design method. Field scans of the 8 target fields demonstrate that acoustic analogues of optical volume holograms can be generated using multi-polymer printing and that these allow the multiplexing of distinct fields onto different incident field directions.

physics.med-ph↗

arXiv2022

j-Wave: An open-source differentiable wave simulator

We present an open-source differentiable acoustic simulator, j-Wave, which can solve time-varying and time-harmonic acoustic problems. It supports automatic differentiation, which is a program transformation technique that has many applications, especially in machine learning and scientific computing. j-Wave is composed of modular components that can be easily customized and reused. At the same time, it is compatible with some of the most popular machine learning libraries, such as JAX and TensorFlow. The accuracy of the simulation results for known configurations is evaluated against the widely used k-Wave toolbox and a cohort of acoustic simulation software. j-Wave is available from https://github.com/ucl-bug/jwave.

physics.comp-ph↗

arXiv2021

A research framework for writing differentiable PDE discretizations in JAX

Differentiable simulators are an emerging concept with applications in several fields, from reinforcement learning to optimal control. Their distinguishing feature is the ability to calculate analytic gradients with respect to the input parameters. Like neural networks, which are constructed by composing several building blocks called layers, a simulation often requires computing the output of an operator that can itself be decomposed into elementary units chained together. While each layer of a neural network represents a specific discrete operation, the same operator can have multiple representations, depending on the discretization employed and the research question that needs to be addressed. Here, we propose a simple design pattern to construct a library of differentiable operators and discretizations, by representing operators as mappings between families of continuous functions, parametrized by finite vectors. We demonstrate the approach on an acoustic optimization problem, where the Helmholtz equation is discretized using Fourier spectral methods, and differentiability is demonstrated using gradient descent to optimize the speed of sound of an acoustic lens. The proposed framework is open-sourced and available at \url{https://github.com/ucl-bug/jaxdf}

cs.LG↗

arXiv2021

High Resolution 3D Ultrasonic Breast Imaging by Time-Domain Full Waveform Inversion

Ultrasound tomography (UST) scanners allow quantitative images of the human breast's acoustic properties to be derived with potential applications in screening, diagnosis and therapy planning. Time domain full waveform inversion (TD-FWI) is a promising UST image formation technique that fits the parameter fields of a wave physics model by gradient-based optimization. For high resolution 3D UST, it holds three key challenges: Firstly, its central building block, the computation of the gradient for a single US measurement, has a restrictively large memory footprint. Secondly, this building block needs to be computed for each of the $10^3-10^4$ measurements, resulting in a massive parallel computation usually performed on large computational clusters for days. Lastly, the structure of the underlying optimization problem may result in slow progression of the solver and convergence to a local minimum. In this work, we design and evaluate a comprehensive computational strategy to overcome these challenges: Firstly, we exploit a gradient computation based on time reversal that dramatically reduces the memory footprint at the expense of one additional wave simulation per source. Secondly, we break the dependence on the number of measurements by using source encoding (SE) to compute stochastic gradient estimates. Also we describe a more accurate, TD-specific SE technique with a finer variance control and use a state-of-the-art stochastic LBFGS method. Lastly, we design an efficient TD multi-grid scheme together with preconditioning to speed up the convergence while avoiding local minima. All components are evaluated in extensive numerical proof-of-concept studies simulating a bowl-shaped 3D UST breast scanner prototype. Finally, we demonstrate that their combination allows us to obtain an accurate 442x442x222 voxel image with a resolution of 0.5mm using Matlab on a single GPU within 24h.

math.NA↗

arXiv2021

Photoacoustic Reconstruction Using Sparsity in Curvelet Frame: Image versus Data Domain

Curvelet frame is of special significance for photoacoustic tomography (PAT) due to its sparsifying and microlocalisation properties. We derive a one-to-one map between wavefront directions in image and data spaces in PAT which suggests near equivalence between the recovery of the initial pressure and PAT data from compressed/subsampled measurements when assuming sparsity in Curvelet frame. As the latter is computationally more tractable, investigation to which extent this equivalence holds conducted in this paper is of immediate practical significance. To this end we formulate and compare DR, a two step approach based on the recovery of the complete volume of the photoacoustic data from the subsampled data followed by the acoustic inversion, and p0R, a one step approach where the photoacoustic image (the initial pressure, p0) is directly recovered from the subsampled data. Effective representation of the photoacoustic data requires basis defined on the range of the photoacoustic forward operator. To this end we propose a novel wedge-restriction of Curvelet transform which enables us to construct such basis. Both recovery problems are formulated in a variational framework. As the Curvelet frame is heavily overdetermined, we use reweighted l1 norm penalties to enhance the sparsity of the solution. The data reconstruction problem DR is a standard compressed sensing recovery problem, which we solve using an ADMMtype algorithm, SALSA. Subsequently, the initial pressure is recovered using time reversal as implemented in the k-Wave Toolbox. The p0 reconstruction problem, p0R, aims to recover the photoacoustic image directly via FISTA, or ADMM when in addition including a non-negativity constraint. We compare and discuss the relative merits of the two approaches and illustrate them on 2D simulated and 3D real data in a fair and rigorous manner.

cs.CV↗

arXiv2021

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.

physics.comp-ph↗

arXiv2019

ElasticMatrix: A MATLAB Toolbox for Anisotropic Elastic Wave Propagation in Layered Media

Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with boundary conditions imposed at each interface. While these methods are well-known, coding the required matrix formation, inversion, and analysis for general multi-layered systems is non-trivial and time-consuming. Here, a new open-source toolbox called ElasticMatrix is described which solves the problem of acoustic and elastic wave propagation in multi-layered media for isotropic and transverse-isotropic materials where the wave propagation occurs in a material plane of symmetry. The toolbox is implemented in MATLAB using an object oriented programming framework and is designed to be easy to use and extend. Methods are provided for calculating and plotting dispersion curves, displacement and stress fields, reflection and transmission coefficients, and slowness profiles.

physics.app-ph↗

arXiv2019

A pseudospectral method for solution of the radiative transport equation

The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently compute numerical solutions to the time-dependent transport equation in arbitrary three-dimensional heterogeneous media with anisotropic scattering. Our GPU-accelerated implementation of the technique is validated by comparison with a Monte-Carlo simulation, demonstrating excellent agreement.

physics.comp-ph↗

arXiv2016

Mesh density functions based on local bandwidth applied to moving mesh methods

Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength mesh density function. This choice is well-justified for piecewise polynomial interpolants, but it is only justified for spectral methods when model solutions include localised steep gradients. In this paper, one-dimensional mesh density functions are presented which are based on a spatially localised measure of the bandwidth of the approximated model solution. In considering bandwidth, these mesh density functions are well-justified for spectral methods, but are not strictly tied to the error properties of any particular spatial interpolant, and are hence widely applicable. The bandwidth mesh density functions are demonstrated by applying periodic spectral and finite-difference moving mesh methods to a number of model problems in acoustics. These problems include a heterogeneous advection equation, the viscous Burgers' equation, and the Korteweg-de Vries equation. Simulation results demonstrate solution convergence rates that are up to an order of magnitude faster using the bandwidth mesh density functions than uniform meshes, and around three times faster than those using the arclength mesh density function.

physics.comp-ph↗

arXiv2016

Acoustic Wave Field Reconstruction from Compressed Measurements with Application in Photoacoustic Tomography

We present a method for the recovery of compressively sensed acoustic fields using patterned, instead of point-by-point, detection. From a limited number of such compressed measurements, we propose to reconstruct the field on the sensor plane in each time step independently assuming its sparsity in a Curvelet frame. A modification of the Curvelet frame is proposed to account for the smoothing effects of data acquisition and motivated by a frequency domain model for photoacoustic tomography. An ADMM type algorithm, SALSA, is used to recover the pointwise data in each individual time step from the patterned measurements. For photoacoustic applications, the photoacoustic image of the initial pressure is reconstructed using time reversal in ${\bf k}$-Wave Toolbox.

math.NA↗

arXiv2016

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.

math.NA↗