Search

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.

There has been an increasing interest in utilizing machine learning methods in inverse problems and imaging. Most of the work has, however, concentrated on image reconstruction problems, and the number of studies regarding the full solution of the inverse problem is limited. In this work, we study a machine learning based approach for the Bayesian inverse problem of photoacoustic tomography. We develop an approach for estimating the posterior distribution in photoacoustic tomography using an approach based on the variational autoencoder. The approach is evaluated with numerical simulations and compared to the solution of the inverse problem using a Bayesian approach.

Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical parameter estimation is an ill-posed inverse problem, and thus it is sensitive to measurement and modeling errors. In this work, we propose a novel way to solve the inverse problem of quantitative photoacoustic tomography based on the perturbation Monte Carlo method. Monte Carlo method for light propagation is a stochastic approach for simulating photon trajectories in a medium with scattering particles. It is widely accepted as an accurate method to simulate light propagation in tissues. Furthermore, it is numerically robust and easy to implement. Perturbation Monte Carlo maintains this robustness and enables forming gradients for the solution of the inverse problem. We validate the method and apply it in the framework of Bayesian inverse problems. The simulations show that the perturbation Monte Carlo method can be used to estimate spatial distributions of both absorption and scattering parameters simultaneously. These estimates are qualitatively good and quantitatively accurate also in parameter scales that are realistic for biological tissues., Comment: 19 pages, 6 figures and supplemental material 4 pages, 2 figures

Mesoporous silicon (PSi) nanoparticles have been widely studied in different biomedical imaging modalities due to their several beneficial material properties. However, they have not been found to be suitable for photoacoustic imaging due to their poor photothermal conversion performance. In the present study, biodegradable black mesoporous silicon (BPSi) nanoparticles with strong light absorbance were developed as superior image contrast agents for photoacoustic tomography (PAT), which was realized with a light-emitting diode (LED) instead of the commonly used laser. LED-based PAT offers the advantages of low cost, compactness, good mobility, and easy operation as compared to the traditional laser-based PAT modality. Nevertheless, the poor imaging sensitivity of the LED-PAT systems has been the main barrier to prevent their wide biomedical application because the LED light has low optical energy. The present study demonstrated that the imaging sensitivity of the LED-PAT system was significantly enhanced with the PEGylated BPSi (PEG-BPSi) nanoparticles. The PEG-BPSi nanoparticles were clearly detectable with a low concentration of 0.05 mg/mL in vitro and with an LED radiation energy of 5.2 μJ. The required concentration of the PEG-BPSi nanoparticles was 10 times lesser than that of the reference gold nanoparticles to reach the corresponding level of the imaging contrast. The ex vivo studies demonstrated that the submillimeter BPSi nanoparticle-based absorbers were distinguishable in chicken breast tissues. The strong contrast provided by the BPSi particles indicated that these particles can be utilized as novel contrast agents in PAT, especially in LED-based systems with low light intensity.

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.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.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.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.The A-SGN method with a norm test can be utilized in QPAT to provide accurate and computationally efficient solutions.

The Fourier transform was compared to conventional temporal moments for time-domain diffuse optical tomography. Both approaches provided similar accuracies. The Fourier transform enabled a computationally cheaper implementation of the inverse solver.

Publisher Copyright: © COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only. 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.

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the so-called Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning, which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the (absolute) absorption and scattering coefficients utilising a ‘model-based’ learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data. We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration.

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.

Inverse problem of estimating initial pressure in photoacoustic tomography is ill-posed and thus sensitive to errors in modelling and measurements. In practical experiments, accurate knowledge of the speed of sound of the imaged target is commonly not available, and therefore an approximate speed of sound is used in the computational model. This can result in errors in the solution of the inverse problem that can appear as artefacts in the reconstructed images. In this paper, the inverse problem of photoacoustic tomography is approached in a Bayesian framework. Errors due to uncertainties in the speed of sound are modelled using Bayesian approximation error modelling. Estimation of the initial pressure distribution together with information on the reliability of these estimates are considered. The approach was studied using numerical simulations. The results show that uncertainties in the speed of sound can cause significant errors in the solution of the inverse problem. However, modelling of these uncertainties improves the accuracy of the solution.

We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the conceptual difficulty to learn such a forward model correction and proceeds to present a possible solution as forward-adjoint correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of Bayesian approximation error method., Comment: 28 pages, 11 Figures

Time-domain diffuse optical tomography (TD-DOT) uses near-infrared pulsed lasers as light sources to measure time-varying exitance on the boundary of the target. These are used to estimate optical properties of the imaged target. Several integral-transform-based moments of the time-resolved data have been utilized in TD-DOT, the most common being the mean time of flight and variance. Recently, it has been shown that Fourier transforming the time-domain data to frequency domain enables utilization of these data at one or several frequencies, producing equally as good estimates as the whole time-domain data. In this work, we present a systematic comparison of the usage of the temporal moments and Fourier transformed data in TD-DOT. Both absolute and difference imaging are evaluated using numerical simulations. The simulations show that utilizing temporal moments and Fourier transformed data in TD-DOT provides good quality reconstructions with a good estimation accuracy. These estimates are improved if more than one data type is used. Furthermore, the simulations show that the frequency-domain computations enable computationally cheaper and straightforward implementation of the inverse solver when compared to the temporal moments.

Diffuse optical tomography (DOT) uses near infrared light for in vivo imaging of spatially varying optical parameters in biological tissues. It is known that time-resolved measurements provide the richest information on soft tissues, among other measurement types in DOT such as steady-state and intensity-modulated measurements. Therefore, several integral-transform-based moments of the time-resolved DOT measurements have been considered to estimate spatially distributed optical parameters. However, the use of such moments can result in low-contrast images and cross-talks between the reconstructed optical parameters, limiting their accuracy. In this work, we propose to utilize a truncated Fourier series approximation in time-resolved DOT. Using this approximation, we obtained optical parameter estimates with accuracy comparable to using whole time-resolved data that uses low computational time and resources. The truncated Fourier series approximation based estimates also displayed good contrast and minimal parameter cross-talk, and the estimates further improved in accuracy when multiple Fourier frequencies were used.

Photoacoustic tomography (PAT) is an imaging modality developed during the past few decades. In the inverse problem of PAT, the aim is to estimate the spatial distribution of an initial pressure p0 generated by the photoacoustic effect, when photoacoustic time-series pt measured on the boundary of the imaged target are given. To produce accurate photoacoustic images, the forward model linking p0 to pt has to model the measurement setup and the underlying physics to a sufficient accuracy. Use of an inaccurate model can lead to significant errors in the solution of the inverse problem. In this work, we study the effect and compensation of modelling errors due to uncertainties in ultrasound sensor locations in PAT using Bayesian approximation error modelling. The approach is evaluated with simulated and experimental data using various levels of measurement noise, uncertainties in sensor locations and varying sensor geometries. The results indicate that even small errors in the modelling of ultrasound sensor locations can lead to large errors in the solution of the inverse problem. Furthermore, the magnitude of these errors is affected by the amount of measurement noise and the measurement The modelling errors can, however, be well compensated by the approximation error modelling.

We present a truncated Fourier series approximation for time-domain diffuse optical tomography. The approach estimated optical parameters with accuracies comparable to using the whole time-resolved data, using very low computational time and resources.

In a thermal tomography measurement setup, a physical body is sequentially heated at different source locations and temperature evolutions are measured at several measurement locations on the surface of the body. Based on these transient measurements, the thermal conductivity, the volumetric heat capacity and the surface heat transfer coefficient of the body are estimated as spatially distributed parameters, typically by minimizing a modified data misfit functional between the measured data and the data computed with the estimated thermal parameters. In thermal tomography, heat transfer is modeled with the time-dependent heat diffusion equation for which direct time domain solving is computationally expensive. In this paper, the computations of thermal tomography are sped up by utilizing a truncated Fourier series approximation approach. In this approach, a frequency domain equivalent of the time domain heat diffusion equation is solved at multiple frequencies and the solutions are used to obtain a truncated Fourier series approximation for the solution and the Jacobian of the time domain heat transfer problem. The feasibility of the approximation is tested with simulated and experimental measurement data. When compared to a previously used time domain approach, it is shown to lead to a significant reduction of computation time in image reconstruction with no significant loss of reconstruction accuracy.

Photoacoustic tomography (PAT) is a hybrid imaging modality that combines optical contrast with ultrasound resolution. Most of the PAT configurations are based on high-energy solid-state lasers such as Nd:YAG laser. In this work, a PAT system that uses light-emitting diode (LED) as a light source is introduced. The system is designed so that the imaged target can be stationary. The target is illuminated by a LED light source from one side and the pressure wave is measured using an acoustic transducer that is rotated around the target. Image reconstruction is based on Bayesian approach to ill-posed inverse problems. The system was tested with light absorbing targets also in limited-view and sparse angle measurement situations. The results show that LED-based instrumentation and advanced reconstruction methods can form a potential PAT system that can also be applied in limited-view and sparse angle photoacoustic tomography., final draft, nonPeerReviewed

Synthetic schlieren tomography is an optical imaging method for characterization of ultrasound fields based on observing bending of light due to acousto-optic effect. In this work, potential optical flow based pressure estimation method is introduced.

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the distribution of optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This optical parameter estimation problem is ill-posed and needs to be approached within the framework of inverse problems. Photoacoustic images are three-dimensional and high-resolution. Furthermore, high-resolution reconstructions of the optical parameters are targeted. Therefore, in order to provide a practical method for quantitative photoacoustic tomography, the inversion algorithm needs to be able to perform successfully with problems of prominent size. In this work, an efficient approach for the inverse problem of quantitative photoacoustic tomography is proposed, assuming an edge-preferring prior for the optical parameters. The method is based on iteratively combining priorconditioned LSQR with a lagged diffusivity step and a linearisation of the measurement model, with the needed multiplications by Jacobians performed in a matrix-free manner. The algorithm is tested with three-dimensional numerical simulations. The results show that the approach can be used to produce accurate and high quality estimates of absorption and diffusion in complex three-dimensional geometries with moderate computation time and cost., Comment: 21 pages, 7 figures

In quantitative photoacoustic tomography, the aim is to reconstruct distributions of optical parameters of an imaged target from an initial pressure distribution obtained from ultrasound measurements. In order to obtain accurate and quantitative information on the optical parameters, modeling light transport in the target is required. Utilizing an approximative model for light transport would be favorable to reduce the computational cost, but the modeling errors of the approximative model can result in significant errors in the reconstructions. In this work, we approach the image reconstruction problem of quantitative photoacoustic tomography in the Bayesian framework. We utilize the Bayesian approximation error method to compensate for the modeling errors between the diffusion approximation and Monte Carlo model for light transport. The approach is studied with two-dimensional numerical simulations with varying optical parameters and noise levels. The results show that Bayesian approximation error method can be used to reduce the effects of the modeling errors in quantitative photoacoustic tomography in a wide range of optical parameters.

Quantitative photoacoustic tomography is a novel imaging method which aims to reconstruct optical parameters of an imaged target based on initial pressure distribution, which can be obtained from ultrasound measurements. In this paper, a method for reconstructing the optical parameters in a Bayesian framework is presented. In addition, evaluating the credibility of the estimates is studied. Furthermore, a Bayesian approximation error method is utilized to compensate the modeling errors caused by coarse discretization of the forward model. The reconstruction method and the reliability of the credibility estimates are investigated with two-dimensional numerical simulations. The results suggest that the Bayesian approach can be used to obtain accurate estimates of the optical parameters and the credibility estimates of these parameters. Furthermore, the Bayesian approximation error method can be used to compensate for the modeling errors caused by a coarse discretization, which can be used to reduce the computational costs of the reconstruction procedure. In addition, taking the modeling errors into account can increase the reliability of the credibility estimates.

The image reconstruction problem (or inverse problem) in photoacoustic tomography is to resolve the initial pressure distribution from detected ultrasound waves generated within an object due to an illumination by a short light pulse. Recently, a Bayesian approach to photoacoustic image reconstruction with uncertainty quantification was proposed and studied with two dimensional numerical simulations. In this paper, the approach is extended to three spatial dimensions and, in addition to numerical simulations, experimental data are considered. The solution of the inverse problem is obtained by computing point estimates, i.e.

The photoacoustic image reconstruction problem (inverse problem) is to estimate an initial acoustic pressure distribution from measurements of ultrasound waves generated within an object due to optical excitation with a short light pulse. In this work, the recently suggested Bayesian approach to photoacoustic tomography is extended to three dimensions and an iterative matrix-free method for the solution of the problem is described. Image reconstruction is investigated with numerical simulations and experimental data. The use of different prior information and noise models in different sensor geometries, including a limited-view setup, is investigated. The results show that the Bayesian approach can produce accurate estimates of the initial pressure distribution even in a limited-view setup provided that prior information and the noise have been properly modelled.

Article, The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light., final draft, http://purl.org/eprint/status/PeerReviewed

Photoacoustic tomography is a hybrid imaging technique that has various applications in biomedicine. In a photoacoustic image reconstruction problem (inverse problem), an initial pressure distribution is reconstructed from measured ultrasound waves which are generated by the photoacoustic effect induced by an optical excitation. In this work, the image reconstruction problem is approached in the framework of Bayesian inversion. The approach is tested with three dimensional numerical simulations. The initial pressure distribution is reconstructed in full-view and limited-view setups. In addition, the reliability of the obtained estimates is assessed. The numerical studies show that accurate estimates of the initial pressure distribution and uncertainty information can be obtained utilizing Bayesian approach.

Quantitative photoacoustic tomography seeks to estimate the optical parameters of a target given photoacoustic measurements as a data. Conventionally the problem is split into two steps: 1) the acoustical inverse problem of estimating the acoustic initial pressure distribution from the acoustical time series data; 2) the optical inverse problem of estimating the optical absorption and scattering from the initial pressure distributions. In this work, an approach for estimating the optical absorption and scattering directly from the acoustical time series is investigated with simulations. The work combines a homogeneous acoustical forward model, based on the Green's function solution of the wave equation, and a finite element method based diffusion approximation model of light propagation into a single forward model. This model maps the optical parameters of interest into a time domain signal. The model is used with a Bayesian approach to ill-posed inverse problems to form estimates of the posterior distributions for the parameters of interest. In addition to being able to provide point estimates of the parameters of interest, i.e. reconstruct the absorption and scattering distributions, the approach can be used to derive information on the uncertainty associated with the estimates.