Abstract
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.
Highlights
Photoacoustic tomography (PAT) is a biomedical imaging modality that has come to prominence over the past two decades due to its ability to provide images of soft tissue based on optical absorption with high spatial resolution
The second condition, known as stress or pressure confinement, is that the characteristic timescale for the acoustic propagation, which will depend on the sound speed and the size of the absorbing regions, must be much slower than the time taken to deposit the optical energy as heat
While variational image reconstruction in PAT has recently been shown to yield superior results compared to time reversal (TR) solutions [5, 17], a potential challenge to its application is that solving (2) by first order optimization methods requires an efficient numerical scheme for the application of the adjoint PAT operator, *
Summary
Photoacoustic tomography (PAT) is a biomedical imaging modality that has come to prominence over the past two decades due to its ability to provide images of soft tissue based on optical absorption with high spatial resolution. Optical absorption contrast is desirable because imaging at multiple wavelengths can in principle provide spectroscopic (chemical) information on the absorbing molecules (chromophores). Due to the highly scattering nature of most biological tissues, imaging purely with light—light in, light out—can only be achieved with high spatial resolution in the vicinity of the tissue surface; beyond that the achievable image resolution falls off quickly with depth. PAT overcomes this problem by generating broadband ultrasonic pulses at the regions of optical absorption which carry the information about the optical contrast to the tissue surface without being scattered significantly. For further references on the experimental aspects and applications of PAT see the review papers [3, 26, 35]
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