Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic Tomography

Rabanser, Simon; Neumann, Lukas; Haltmeier, Markus

doi:10.3390/e20020121

Cited by 8 publications

(9 citation statements)

References 60 publications

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“…where acoustic measurement generated by the photoacoustic effect is used to infer the optimal properties of the media. In this case, an improved stability is anticipated [37,38].…”

Section: Research Results and Discussionmentioning

confidence: 97%

Bayesian Instability of Optical Imaging: Ill Conditioning of Inverse Linear and Nonlinear Radiative Transfer Equation in the Fluid Regime

Newton

Wang

2022

Computation

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For the inverse problem in physical models, one measures the solution and infers the model parameters using information from the collected data. Oftentimes, these data are inadequate and render the inverse problem ill-posed. We study the ill-posedness in the context of optical imaging, which is a medical imaging technique that uses light to probe (bio-)tissue structure. Depending on the intensity of the light, the forward problem can be described by different types of equations. High-energy light scatters very little, and one uses the radiative transfer equation (RTE) as the model; low-energy light scatters frequently, so the diffusion equation (DE) suffices to be a good approximation. A multiscale approximation links the hyperbolic-type RTE with the parabolic-type DE. The inverse problems for the two equations have a multiscale passage as well, so one expects that as the energy of the photons diminishes, the inverse problem changes from well- to ill-posed. We study this stability deterioration using the Bayesian inference. In particular, we use the Kullback–Leibler divergence between the prior distribution and the posterior distribution based on the RTE to prove that the information gain from the measurement vanishes as the energy of the photons decreases, so that the inverse problem is ill-posed in the diffusive regime. In the linearized setting, we also show that the mean square error of the posterior distribution increases as we approach the diffusive regime.

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“…where acoustic measurement generated by the photoacoustic effect is used to infer the optimal properties of the media. In this case, an improved stability is anticipated [37,38].…”

Section: Research Results and Discussionmentioning

confidence: 97%

Bayesian Instability of Optical Imaging: Ill Conditioning of Inverse Linear and Nonlinear Radiative Transfer Equation in the Fluid Regime

Newton

Wang

2022

Computation

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“…Therefore, utilizing multi-measurement to iterate µ a,xf is expected improve the algorithm stability. As for algorithm 1 and algorithm 3, corresponding iteration scheme (15), (16) and (24), (25) can be respectively replaced by µ a,xf i`1 " 1 1´η˜p ( 29) and µ a,xf i`1 " 1 1´η˜p…”

Section: Multi-measurement Casementioning

confidence: 99%

A hybrid reconstruction approach for absorption coefficient by fluorescence photoacoustic tomography

Wang¹,

Zhou²

2018

Inverse Problems

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In this paper, we propose a hybrid method to reconstruct the absorption coefficient by fluorescence photoacoustic tomography (FPAT), which combines a squeeze iterative method (SIM) and a nonlinear optimization method. The SIM is to use two monotonic sequences to squeeze the exact coefficient, and it quickly locates near the exact coefficient. The nonlinear optimization method is utilized to attain a higher accuracy. The hybrid method inherits the advantages of each method with higher accuracy and faster convergence. The hybrid reconstruction method is also suitable for multi-measurement. Numerical experiments show that the hybrid method converges faster than the optimization method in multi-measurement case, and that the accuracy is also higher in onemeasurement case.

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“…Alternatively, a joint optimization approach can solve this issue. 36,37 The measured EIR is refined with a variable projection method to recover the optical deposition by exploiting the bi-linearity of the imaging model. 32,33 This approach enables low-cost and adequate compensation for the model mismatch.…”

Section: Introductionmentioning

confidence: 99%

Image reconstruction for endoscopic photoacoustic tomography including effects of detector responses

Sun

2022

Exp Biol Med (Maywood)

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In photoacoustic tomography (PAT), conventional image reconstruction methods are generally based on the assumption of an ideal point-like ultrasonic detector. This assumption is appropriate when the receiving surface of the detector is sufficiently small and/or the distance between the imaged object and the detector is large enough. However, it does not hold in endoscopic applications of PAT. In this study, we propose a model-based image reconstruction method for endoscopic photoacoustic tomography (EPAT), considering the effect of detector responses on image quality. We construct a forward model to physically describe the imaging process of EPAT, including the generation of the initial pressure due to optical absorption and thermoelastic expansion, the propagation of photoacoustic waves in tissues, and the acoustic measurement. The model outputs the theoretical sampling voltage signal, which is the response of the ultrasonic detector to the acoustic pressure reaching its receiving surface. The images representing the distribution map of the optical absorption energy density on cross-sections of the imaged luminal structures are reconstructed from the sampling voltage signals output by the detector through iterative inversion of the forward model. Compared with the conventional approaches based on back-projection and other imaging models, our method improved the quality and spatial resolution of the resulting images.

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Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic Tomography

Cited by 8 publications

References 60 publications

Bayesian Instability of Optical Imaging: Ill Conditioning of Inverse Linear and Nonlinear Radiative Transfer Equation in the Fluid Regime

Bayesian Instability of Optical Imaging: Ill Conditioning of Inverse Linear and Nonlinear Radiative Transfer Equation in the Fluid Regime

A hybrid reconstruction approach for absorption coefficient by fluorescence photoacoustic tomography

Image reconstruction for endoscopic photoacoustic tomography including effects of detector responses

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