Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distributions in Photoacoustic Computed Tomography: A Numerical Investigation

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 alternatively 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.

Generation of anatomically realistic numerical phantoms for photoacoustic and ultrasonic breast imaging

“…This is consistent with previous Note: μ a , optical absorption coefficient; μ s , optical scattering coefficient; g, scattering anisotropy; n, refractive index. studies [7][8][9][10]12 that have demonstrated that consideration of the acoustic properties of the medium is necessary for accurate PACT image reconstruction.…”

“…Both PACT and USCT are radiation-free, breast-compressionfree, and relatively inexpensive. In addition, the integration of PACT and USCT has drawn increasing attention [7][8][9][10][11] because they provide complementary contrasts, the speed of sound information produced by USCT can improve the accuracy of PACT image reconstruction, and the two imaging modalities can share a common ultrasonic detection system. These advantages make PACT and USCT promising tools for breast cancer screening.…”

Joint reconstruction of the initial pressure and speed of sound distributions from combined photoacoustic and ultrasound tomography measurements

“…In practice, the SOS distribution is typically unknown. Further, it has been shown that, in general, the SOS and initial pressure distributions cannot both be stably recovered from PACT measurements alone [21, 22]. …”

“…An estimate of the initial pressure distribution can be obtained by solving the penalized least-squares optimization problem [17, 22, 37], $${\widehat{\mathrm{boldp}}}_0=\underset{{\mathbf{p}}_0\ge 0}{\text{arg min}}{F}_{p}false({\mathbf{p}}_0,\mathrm{boldc}false)+\lambda {ℛ}_{p}false({\mathbf{p}}_{0}false),$$where F p ( p 0 , c ) is a data fidelity term, ℛ p ( p 0 ) is a regularization function, and λ p is a regularization parameter, which controls the relative weight of the ℛ p ( p 0 ) term, Here, F p ( p 0 , c ) is given by $$F_{p}false({\mathbf{p}}_{0}false)\mathrm{boldc}false)\equiv \frac{1}{2}{false\Vert \underset{¯}{{\mathrm{boldg}}_{\text{italicpa}}}-{\mathbf{\text{MH}}}_{\mathit{\text{pa}}}false(\mathrm{boldc}false){\mathbf{p}}_{0}false\Vert }_2^2,$$where $\underset{¯}{{\mathrm{boldg}}_{\text{italicpa}}}\in {ℝ}^{N^{\mathit{\text{rec}}}L}$ is the measured data. For this problem, the data fidelity term is differentiable and convex with respect to p 0 .…”

“…One method to estimate the SOS distribution, in the absence of adjunct imaging data (e.g. USCT measurements), is to jointly estimate the SOS and initial pressure distributions from the PACT data alone [22, 39, 40]. This can be performed by solving the following optimization problem [22], $${\widehat{\mathrm{boldp}}}_0,\hat{\mathbf{c}}=\underset{{\mathbf{p}}_0\ge 0,\mathrm{boldc}}{\text{arg min}}{F}_{p}false({\mathbf{p}}_0,\mathrm{boldc}false)+{\lambda }_p{ℛ}_{p}false({\mathbf{p}}_{0}false)+{\lambda }_c{ℛ}_{c}false(\mathrm{boldc}false),$$where ℛ c ( c ) is a regularization function for the SOS and λ c is its corresponding regularization parameter value.…”