Abstract:
The standard approach for photoacoustic imaging with variable speed of sound is time reversal, which consists in solving a well-posed final-boundary value problem for the wave equation backwards in time. This paper investigates the iterative Landweber regularization algorithm, where convergence is guaranteed by standard regularization theory, notably also in cases of trapping sound speed or for short measurement times. We formulate and solve the direct and inverse problem on the whole Euclidean space, what is common in standard photoacoustic imaging, but not for time-reversal algorithms, where the problems are considered on a domain enclosed by the measurement devices. We formulate both the direct and adjoint photoacoustic operator as the solution of an interior and an exterior differential equation which are coupled by transmission conditions. The prior is solved numerically using a Galerkin scheme in space and finite difference discretization in time, while the latter consists in solving a boundary integral equation. We therefore use a BEM-FEM approach for numerical solution of the forward operators. We analyze this method, prove convergence, and provide numerical tests. Moreover, we compare the approach to time reversal.

Abstract:
In most photoacoustic (PA) measurements, variations in speed-of-sound (SOS) of the subject are neglected under the assumption of acoustic homogeneity. Biological tissue with spatially heterogeneous SOS cannot be accurately reconstructed under this assumption. We present experimental and image reconstruction methods with which 2-D SOS distributions can be accurately acquired and reconstructed, and with which the SOS map can be used subsequently to reconstruct highly accurate PA tomograms. We begin with a 2-D iterative reconstruction approach in an ultrasound transmission tomography (UTT) setting, which uses ray refracted paths instead of straight ray paths to recover accurate SOS images of the subject. Subsequently, we use the SOS distribution in a new 2-D iterative approach, where refraction of rays originating from PA sources are accounted for in accurately retrieving the distribution of these sources. Both the SOS reconstruction and SOS-compensated PA reconstruction methods utilize the Eikonal equation to model acoustic wavefront propagation, which is solved using a high accuracy fast marching method (HAFMM). We validate the new reconstruction algorithms using numerical phantoms. For experiments we use the PER-PACT method which can be used to simultaneously acquire SOS and PA data from subjects. We test the reconstruction algorithms using experimental data acquired with the PER-PACT setup from challenging physical phantoms. The results show that it is important to take SOS inhomogeneities into account. The iterative reconstruction algorithms, that model acoustic refractive effects, yield artifact-free highly accurate images. Our approach of using the hybrid measurement method and the new reconstruction algorithms, is successful in substantially improving the quality of PA images with a minimization of blurring and artefacts.

Abstract:
We present a new algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature of the problem. We work with variable sound speeds that might be also discontinuous across some surface. The latter problem arises in brain imaging. The new algorithm is based on an explicit formula in the form of a Neumann series. We present numerical examples with non-trapping, trapping and piecewise smooth speeds, as well as examples with data on a part of the boundary. These numerical examples demonstrate the robust performance of the new algorithm.

Abstract:
Photoacoustic computed tomography (PACT) is a rapidly emerging bioimaging modality that seeks to reconstruct an estimate of the absorbed optical energy density within an object. Conventional PACT image reconstruction methods assume a constant speed-of-sound (SOS), which can result in image artifacts when acoustic aberrations are significant. It has been demonstrated that incorporating knowledge of an object's SOS distribution into a PACT image reconstruction method can improve image quality. However, in many cases, the SOS distribution cannot be accurately and/or conveniently estimated prior to the PACT experiment. Because variations in the SOS distribution induce aberrations in the measured photoacoustic wavefields, certain information regarding an object's SOS distribution is encoded in the PACT measurement data. Based on this observation, a joint reconstruction (JR) problem has been proposed in which the SOS distribution is concurrently estimated along with the sought-after absorbed optical energy density from the photoacoustic measurement data. A broad understanding of the extent to which the JR problem can be accurately and reliably solved has not been reported. In this work, a series of numerical experiments is described that elucidate some important properties of the JR problem that pertain to its practical feasibility. To accomplish this, an optimization-based formulation of the JR problem is developed that yields a non-linear iterative algorithm that alternatingly updates the two image estimates. Heuristic analytic insights into the reconstruction problem are also provided. These results confirm the ill-conditioned nature of the joint reconstruction problem that will present significant challenges for practical applications.

Abstract:
Context. The anelastic approximation is often adopted in numerical calculation with low Mach number, such as stellar internal convection. This approximation requires frequent global communication, because of an elliptic partial differential equation. Frequent global communication is negative factor for the parallel computing with a large number of CPUs. Aims. The main purpose of this paper is to test the validity of a method that artificially reduces the speed of sound for the compressible fluid equations in the context of stellar internal convection. The reduction of speed of sound allows for larger time steps in spite of low Mach number, while the numerical scheme remains fully explicit and the mathematical system is hyperbolic and thus does not require frequent global communication. Methods. Two and three dimensional compressible hydrodynamic equations are solved numerically. Some statistical quantities of solutions computed with different effective Mach numbers (due to reduction of speed of sound) are compared to test the validity of our approach. Results. Numerical simulations with artificially reduced speed of sound are a valid approach as long as the effective Mach number (based on the reduced speed of sound) remains less than 0.7.

Abstract:
The paper contains a simple approach to reconstruction in Thermoacoustic and Photoacoustic Tomography. The technique works for any geometry of point detectors placement and for variable sound speed satisfying a non-trapping condition. A uniqueness of reconstruction result is also obtained.

Abstract:
Photoacoustic spectroscopy (PAS) is an unusual form of spectroscopy using Light and Sound. PAS is based on the absorption of electromagnetic radiation by analyte molecules.The absorbed energy is measured by detecting pressure fluctuations in the form of Sound waves or shock pulses. It is a non-destructive technique that is applicable to almost all types of samples. PAS offers minimal or no sample preparation, the ability to look at opaque and scattering sample and the capability to perform depth profiling experiment. These features mean that PAS can be used for on-line monitoring of various gases and also in depth-resolved characterization of materials. PAS is also finding wide application in analysis of biological materials such as blood, skin, tumors, etc.

Abstract:
In this paper we propose an approach for \emph{simultaneous} identification of the \emph{absorption density} and the \emph{speed of sound} by photoacoustic measurements. Experimentally our approach can be realized with sliced photoacoustic experiments. The mathematical model for such an experiment is developed and exact reconstruction formulas for both parameters are presented.

Abstract:
We consider the mathematical model of photoacoustic and thermoacoustic tomography in media with a variable sound speed. When the sound speed is known, the explicit reconstruction formula by P. Stefanov and G. Uhlmann (Inverse Problems, 25(7):075011, 16, 2009) can be used. We study how a modelling error in the sound speed affects the reconstruction formula and quantify the effect in terms of a stability estimate.

Abstract:
We performed 3D numerical simulations of the solar surface wave field for the quiet Sun and for three models with different localized sound-speed variations in the interior with: (i) deep, (ii) shallow, and (iii) two-layer structures. We used simulated data generated by two different codes which use the same standard solar model as a background model, but utilize two different integration techniques and use different models of stochastic wave excitation. Acoustic travel times were measured from all data sets using the time-distance helioseismology technique and compared with the ray theory predictions, frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the ray theory in both cases with and without phase-speed filtering for the shallow and deep perturbations. This testing verifies the whole measuring-filtering-inversion procedure for sound-speed anomalies inside the Sun. It is shown, that the phase-speed filtering, frequently used to improve the signal-to-noise ratio does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the background sound-speed profiles in all cases. Due to its smoothing nature, the inversion procedure overestimates sound speed variations in areas with sharp gradients of the sound-speed profile.