Photoacoustic image reconstruction in an attenuating medium using singular-value decomposition

Model-Based Reconstruction of Large Three-Dimensional Optoacoustic Datasets

Iterative model-based algorithms are known to enable more accurate and quantitative optoacoustic (photoacoustic) tomographic reconstructions than standard back-projection methods. However, three-dimensional (3D) model-based inversion is often hampered by high computational complexity and memory overhead. Parallel implementations on a graphics processing unit (GPU) have been shown to efficiently reduce the memory requirements by on-the-fly calculation of the actions of the optoacoustic model matrix, but the high complexity still makes these approaches impractical for large 3D optoacoustic datasets. Herein, we show that the computational complexity of 3D model-based iterative inversion can be significantly reduced by splitting the model matrix into two parts: one maximally sparse matrix containing only one entry per voxel-transducer pair and a second matrix corresponding to cyclic convolution. We further suggest reconstructing the images by multiplying the transpose of the model matrix calculated in this manner with the acquired signals, which is equivalent to using a very large regularization parameter in the iterative inversion method. The performance of these two approaches is compared to that of standard back-projection and a recently introduced GPU-based model-based method using datasets from in vivo experiments. The reconstruction time was accelerated by approximately an order of magnitude with the new iterative method, while multiplication with the transpose of the matrix is shown to be as fast as standard back-projection.

A survey of computational frameworks for solving the acoustic inverse problem in three-dimensional photoacoustic computed tomography

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging technique that holds great promise for biomedical imaging. PACT is a hybrid imaging method that can exploit the strong endogenous contrast of optical methods along with the high spatial resolution of ultrasound methods. In its canonical form that is addressed in this article, PACT seeks to estimate the photoacoustically-induced initial pressure distribution within the object. Image reconstruction methods are employed to solve the acoustic inverse problem associated with the image formation process. When an idealized imaging scenario is considered, analytic solutions to the PACT inverse problem are available; however, in practice, numerous challenges exist that are more readily addressed within an optimization-based, or iterative, image reconstruction framework. In this article, the PACT image reconstruction problem is reviewed within the context of modern optimization-based image reconstruction methodologies. Imaging models that relate the measured photoacoustic wavefields to the sought-after object function are described in their continuous and discrete forms. The basic principles of optimization-based image reconstruction from discrete PACT measurement data are presented, which includes a review of methods for modeling the PACT measurement system response and other important physical factors. Non-conventional formulations of the PACT image reconstruction problem, in which acoustic parameters of the medium are concurrently estimated along with the PACT image, are also introduced and reviewed.

Frequency analysis for an extended photoacoustic transport model

In photoacoustic imaging, the signal attenuation is a well-known source of artifacts over the image reconstruction. It is recognized that this is caused by optical absorption effects and by the ultrasound broadband scattering. However, the sound dispersion is generally neglected, although it appears notably in thick or heterogeneous tissues. In the present Letter, we give an experimental example in which both attenuation and sound dispersion are dealt with as relevant features to be taken into consideration. An analytic perspective of these perturbations leads us to a waveform transport-model extension that provides a linear description of the induced acoustic effects. We find a near match between the theoretical predictions and the experimental results in the frequency domain. These outcomes approximate projection data that represent forward solutions in photoacoustic image reconstruction.