Image reconstruction in photoacoustic tomography with heterogeneous media using an iterative method

There remains an urgent need to develop effective photoacoustic computed tomography (PACT) image recon- struction methods for use with acoustically inhomogeneous media. Transcranial PACT brain imaging is an im- portant example of an emerging imaging application that would benefit greatly from this. Existing approaches to PACT image reconstruction in acoustically heterogeneous media are limited to weakly varying media, are computationally burdensome, and/or make impractical assumptions regarding the measurement geometry. In this work, we develop and investigate a full-wave approach to iterative image reconstruction in PACT for media possessing inhomogeneous speed-of-sound and mass density distributions. A key contribution of the work is the formulation of a procedure to implement a matched discrete forward and backprojection operator pair, which facilitates the application of a wide range of modern iterative image reconstruction algorithms. This presents the opportunity to employ application-specific regularization methods to mitigate image artifacts due to mea- surement data incompleteness and noise. Our results establish that the proposed image reconstruction method can effectively compensate for acoustic aberration and reduces artifacts in the reconstructed image

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.Comment: submitted to "Inverse Problems

Image reconstruction in photoacoustic tomography with heterogeneous media using an iterative method

There remains an urgent need to develop effective photoacoustic computed tomography (PACT) image recon- struction methods for use with acoustically inhomogeneous media. Transcranial PACT brain imaging is an im- portant example of an emerging imaging application that would benefit greatly from this. Existing approaches to PACT image reconstruction in acoustically heterogeneous media are limited to weakly varying media, are computationally burdensome, and/or make impractical assumptions regarding the measurement geometry. In this work, we develop and investigate a full-wave approach to iterative image reconstruction in PACT for media possessing inhomogeneous speed-of-sound and mass density distributions. A key contribution of the work is the formulation of a procedure to implement a matched discrete forward and backprojection operator pair, which facilitates the application of a wide range of modern iterative image reconstruction algorithms. This presents the opportunity to employ application-specific regularization methods to mitigate image artifacts due to mea- surement data incompleteness and noise. Our results establish that the proposed image reconstruction method can effectively compensate for acoustic aberration and reduces artifacts in the reconstructed image

Mitigation of artifacts due to isolated acoustic heterogeneities in photoacoustic computed tomography using a variable data truncation-based reconstruction method

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the absorbed optical energy density within tissue. If the object possesses spatially variant acoustic properties that are unaccounted for by the reconstruction method, the estimated image can contain distortions. While reconstruction methods have recently been developed to compensate for this effect, they generally require the object's acoustic properties to be known a priori. To circumvent the need for detailed information regarding an object's acoustic properties, we previously proposed a half-time reconstruction method for PACT. A half-time reconstruction method estimates the PACT image from a data set that has been temporally truncated to exclude the data components that have been strongly aberrated. However, this method can be improved upon when the approximate sizes and locations of isolated heterogeneous structures, such as bones or gas pockets, are known. To address this, we investigate PACT reconstruction methods that are based on a variable data truncation (VDT) approach. The VDT approach represents a generalization of the half-time approach, in which the degree of temporal truncation for each measurement is determined by the distance between the corresponding ultrasonic transducer location and the nearest known bone or gas void location. Computer-simulated and experimental data are employed to demonstrate the effectiveness of the approach in mitigating artifacts due to acoustic heterogeneities

A Multi-Grid Iterative Method for Photoacoustic Tomography

Inspired by the recent advances on minimizing nonsmooth or bound-constrained convex functions on models using varying degrees of fidelity, we propose a line search multigrid (MG) method for full-wave iterative image reconstruction in photoacoustic tomography (PAT) in heterogeneous media. To compute the search direction at each iteration, we decide between the gradient at the target level, or alternatively an approximate error correction at a coarser level, relying on some predefined criteria. To incorporate absorption and dispersion, we derive the analytical adjoint directly from the first-order acoustic wave system. The effectiveness of the proposed method is tested on a total-variation penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated variant (FISTA), which have been used in many studies of image reconstruction in PAT. The results show the great potential of the proposed method in improving speed of iterative image reconstruction

Full field inversion in photoacoustic tomography with variable sound speed

Recently, a novel measurement setup has been introduced to photoacoustic tomography, that collects data in the form of projections of the full 3D acoustic pressure distribution at a certain time instant. Existing imaging algorithms for this kind of data assume a constant speed of sound. This assumption is not always met in practice and thus leads to erroneous reconstructions. In this paper, we present a two-step reconstruction method for full field detection photoacoustic tomography that takes variable speed of sound into account. In the first step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data. In the second step, one solves a final time wave inversion problem where the initial pressure distribution is recovered from the known pressure distribution at the measurement time. For the latter problem, we derive an iterative solution approach, compute the required adjoint operator, and show its uniqueness and stability