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.

An adaptive stochastic Gauss-Newton method for reconstructing absorption and scattering coefficients in optical tomography using the Monte Carlo method for light transport was developed. Based on numerical simulations, the method provides reconstructions with good accuracy. (c) 2025 The Author(s)

In this work, the optical inverse problem of quantitative photoacoustic tomography is studied. Maximum a posteriori estimates for absorption and scattering are computed from absorbed energy density, and the reliability of the estimates is evaluated utilizing the Laplace's approximation. The forward operator and evaluation of the search direction in the minimization algorithm are based on the Monte Carlo method for light transport. Monte Carlo is a stochastic method where the solution of a light transport model is approximated by simulating paths of photon packets as they undergo absorption and scattering events in a scattering medium. This makes evaluation of the search direction also stochastic. In this work, we study an adaptive approach where the number of simulated photon packets on each iteration is determined by utilizing a so-called norm test. In the norm test, the variance of the gradient of the objective function is assessed and used to control the number of photon packets. The approach is studied with numerical simulations. The results show that the adaptive approach can be used to control the number of photon packets during an iterative solution of the inverse problem of quantitative photoacoustic tomography. Further, the adaptive approach can reduce the computational cost compared to a conventional approach where the number of photon packets is fixed.

In quantitative photoacoustic tomography, the optical parameters of a target, most importantly the concentrations of chromophores such as deoxygenated and oxygenated hemoglobin, are estimated from photoacoustic data measured on the boundary of the target. In this work, a numerical approximation of a forward model for spectral quantitative photoacoustic tomography is constructed by utilizing the diffusion approximation for light propagation, the acoustic wave equation for ultrasound propagation, and spectral models of optical absorption and scattering to describe the wavelength dependence of the optical parameters. The related inverse problem is approached in the framework of Bayesian inverse problems. Concentrations of four chromophores (deoxygenated and oxygenated hemoglobin, water, and lipid), two scattering parameters (reference scattering and scattering power), and the Grüneisen parameter are estimated in a single-stage from photoacoustic data. The methodology is evaluated using numerical simulations in different full-view and limited-view imaging settings. The results show that, utilizing spectral data and models, the spectral optical parameters and the Grüneisen parameter can be simultaneously estimated. Furthermore, the approach can also be utilized in limited-view imaging situations.

Objective . In this paper, we propose positron emission tomography image reconstruction using a multi-resolution triangular mesh. The mesh can be adapted based on patient specific anatomical information that can be in the form of a computed tomography or magnetic resonance imaging image in the hybrid imaging systems. The triangular mesh can be adapted to high resolution in localized anatomical regions of interest (ROI) and made coarser in other regions, leading to an imaging model with high resolution in the ROI with clearly reduced number of degrees of freedom compared to a conventional uniformly dense imaging model. Approach. We compare maximum likelihood expectation maximization reconstructions with the multi-resolution model to reconstructions using a uniformly dense mesh, a sparse mesh and regular rectangular pixel mesh. Two simulated cases are used in the comparison, with the first one using the NEMA image quality phantom and the second the XCAT human phantom. Main results. When compared to the results with the uniform imaging models, the locally refined multi-resolution mesh retains the accuracy of the dense mesh reconstruction in the ROI while being faster to compute than the reconstructions with the uniformly dense mesh. The locally dense multi-resolution model leads also to more accurate reconstruction than the pixel-based mesh or the sparse triangular mesh. Significance. The findings suggest that triangular multi-resolution mesh, which can be made patient and application specific, is a potential alternative for pixel-based reconstruction.

A global effort towards improved quantitative understanding of greenhouse gas emissions is taking pace. This includes developing source identification, quantification, and apportionment in an attempt to understand global budget and trends, but also developing monitoring systems making emission reduction commitment verifiable. In this context, we demonstrate a novel approach to continuous methane emission monitoring at the spatial scale of an industrial facility. By combining multi-directional measurements of path-integrated methane concentrations with Bayesian state estimation, we show a realistic tomographic gas plume reconstruction, its evolution in time, and the associated estimation of the source map. The method is validated using measurements from controlled methane releases over a domain of area 120×40 m2. For the first demonstration, a two dimensional geometry has been used in the gas flow model; nevertheless, sources are located within 3 to 12 meters, and mass emission rates are estimated within <30% for 80% of the cases.

Image reconstruction in optical tomography in the so-called transport regime, where the diffusion approximation is not valid, requires modeling of light transport using the radiative transfer equation. In this work, we approach this problem by utilizing the Monte Carlo method for light transport. In this work, we propose a methodology for absolute imaging of absorption and scattering in this regime utilizing a Monte Carlo method for light transport. The image reconstruction problem is formulated as a minimization problem that is solved using a stochastic Gauss-Newton method. In the construction of the Jacobian matrix for scattering, a perturbation approximation for Monte Carlo is utilized. The approach is evaluated with numerical simulations using an adaptive approach where the number of photon packets is adjusted during the iterations, and with different fixed numbers of photon packets. The simulations show that the Monte Carlo method for light transport can be utilized in the absolute imaging problem of optical tomography and that the absorption and scattering parameters can be estimated simultaneously with good accuracy.

In quantitative photoacoustic tomography (QPAT), distributions of optical parameters inside the target are reconstructed from photoacoustic images. In this work, we utilize the Monte Carlo (MC) method for light transport in the image reconstruction of QPAT. Modeling light transport accurately with the MC requires simulating a large number of photon packets, which can be computationally expensive. On the other hand, too low number of photon packets results in a high level of stochastic noise, which can lead to significant errors in reconstructed images. In this work, we use an adaptive approach, where the number of simulated photon packets is adjusted during an iterative image reconstruction. It is based on a norm test where the expected relative error of the minimization direction is controlled. The adaptive approach automatically determines the number of simulated photon packets to provide sufficiently accurate light transport modeling without unnecessary computational burden. The presented approach is studied with two-dimensional simulations.

Quantitative photoacoustic tomography aims at estimating optical parameters of tissue utilizing the photoacoustic effect. In this work, spectral optical parameters are estimated in one-step from photoacoustic data utilizing a Bayesian approach to inverse problems. Forward model is constructed by presenting optical absorption and scattering by their spectral representations, and by combining the models for light and ultrasound propagation. The proposed methodology is evaluated with numerical simulations in full view and limited view geometries.

Background-oriented schlieren imaging is a recently proposed noninvasive optical method for imaging of full ultrasound fields. In this work, the impact of uncertainty in geometrical parameters of a background-oriented schlieren measurement setup for imaging of full ultrasound fields is studied using numerical simulations. The studied parameters are focal length of the camera and positions and orientations of the camera, water tank, and ultrasound field. The results demonstrate that the most sensitive parameters affecting the accuracy of the reconstructed ultrasound fields are the orientations of the camera that change the direction of an effective optical axis. Other sensitive parameters are the focal length of the camera and the position of the ultrasound field in perpendicular directions of an optical axis. This synthetic study demonstrates the accuracy requirements for calibrating the geometrical parameters of a measurement setup that would be required to achieve accuracy comparable to that of hydrophone measurements using the background-oriented schlieren imaging. Explicitly, limits of the variation ranges of the geometrical parameters resulting in relative error ranges of 5% and 10% are given. The results of this study may contribute to help design future background-oriented schlieren measurement setups intended for measurement of full ultrasound fields.

Abstract. Significance: The image reconstruction problem in quantitative photoacoustic tomography (QPAT) is an ill-posed inverse problem. Monte Carlo method for light transport can be utilized in solving this image reconstruction problem. Aim: The aim was to develop an adaptive image reconstruction method where the number of photon packets in Monte Carlo simulation is varied to achieve a sufficient accuracy with reduced computational burden. Approach: The image reconstruction problem was formulated as a minimization problem. An adaptive stochastic Gauss–Newton (A-SGN) method combined with Monte Carlo method for light transport was developed. In the algorithm, the number of photon packets used on Gauss–Newton (GN) iteration was varied utilizing a so-called norm test. Results: The approach was evaluated with numerical simulations. With the proposed approach, the number of photon packets needed for solving the inverse problem was significantly smaller than in a conventional approach where the number of photon packets was fixed for each GN iteration. Conclusions: The A-SGN method with a norm test can be utilized in QPAT to provide accurate and computationally efficient solutions.

Background-oriented schlieren imaging is a recently proposed method for measuring projections of ultrasound fields. The method is based on observing deflection of light in a heterogeneous refractive index field that is induced by ultrasound via an acousto-optic effect. The deflection of light manifests as apparent perturbations in an imaged target, forming a potential flow estimation problem. In this work, the potential flow approach is formulated as a nonlinear regularized least-squares approach to alleviate limitations of approaches that linearize the problem. The nonlinear approach is shown to outperform the linear one when estimating projections of medically relevant ultrasound fields.

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

In this work, the inverse problem problem of quantitative photoacoustic tomography is approached in a Bayesian framework. Modeling errors caused by an approximative light transport model are compensated by utilizing Bayesian approximation error modeling.

Photoacoustic tomography (PAT) is an imaging modality that utilizes the photoacoustic effect. In PAT, a photoacoustic image is computed from measured data by modeling ultrasound propagation in the imaged domain and solving an inverse problem utilizing a discrete forward operator. However, in realistic measurement geometries with several ultrasound transducers and relatively large imaging volume, an explicit formation and use of the forward operator can be computationally prohibitively expensive. In this work, we propose a transformation-based approach for efficient modeling of photoacoustic signals and reconstruction of photoacoustic images. In the approach, the forward operator is constructed for a reference ultrasound transducer and expanded into a general measurement geometry using transformations that map the formulated forward operator in local coordinates to the global coordinates of the measurement geometry. The inverse problem is solved using a Bayesian framework. The approach is evaluated with numerical simulations and experimental data. The results show that the proposed approach produces accurate 3-D photoacoustic images with a significantly reduced computational cost both in memory requirements and time. In the studied cases, depending on the computational factors, such as discretization, over the 30-fold reduction in memory consumption was achieved without a reduction in image quality compared to a conventional approach.

In this work, use of perturbation Monte Carlo is extended to solving inverse problem of quantitative photoacoustic tomography. The approach is demonstrated feasible for estimating optical absorption and scattering distribution.

In this work, a computationally efficient forward model for photoacoustic tomography is presented. The approach is able to produce accurate photoacoustic images with significantly reduced computational cost compared to a conventional approach.