Photoacoustic tomography (PAT) is an emerging soft-tissue imaging modality that has great potential for a wide range of biomedical imaging applications.  It can be viewed as a hybrid imaging modality in the sense that it utilizes an optical contrast mechanism combined with ultrasonic detection principles, thereby combining the advantages of optical and ultrasonic imaging while circumventing their primary limitations. The goal of PAT is to reconstruct the distribution of an object's absorbed optical energy density from measurements of pressure wavefields that are induced via the thermoacoustic effect.  In this talk, we review our recent advancements in practical image reconstruction approaches for PAT in heterogeneous acoustic media.  Such advancements include physics-based models of the measurement process and associated inversion methods for reconstructing images from limited data sets.  Applications of PAT to transcranial brain imaging are presented.

Many techniques developed for free-discontinuity problems, arising for example in imaging or in fracture mechanics, may be successfully applied to reconstruction methods for inverse problems whose unknowns may be characterized by discontinuous functions.

We show the validity of this approach both from the theoretical point of view, by a convergence analysis, and from the numerical point of view.

Waves reflecting/refracting/transmitting from singularities of a metric (e.g. sound speed) satisfy the law of reflection. One expects that if the singularities are sufficiently weak, in terms of differentiability (conormal order) then the reflected singularity is weaker than the transmitted one, in the sense that it is more regular. In this joint work with Maarten de Hoop and Gunther Uhlmann we prove such a result with slightly more regular than C^1 metrics.

We present a numerical study of the quantitative photoacoustic
tomography problem with the transport model, aiming at reconstructing simultaneously the absorption, scattering and Gr\"uneisen coefficients with interior data. We study the effect of the amount of data on the quality of the reconstructions, and investigate related uniqueness and non-uniqueness issues. We propose simple reconstruction procedures in some specific cases. Numerical simulations with synthetic data will be presented.

On the basis of the subspace-based optimization method (SOM), a twofold SOM (TSOM) and its variation, the FFT-TSOM, are proposed to solve in a more stable and more efficient manner the two-dimensional (2D) and three-dimensional (3D) electromagnetic inverse scattering problems. In the SOM, part of the induced current is found directly from the measured scattered fields while the remaining is searched within a current subspace, which has small contribution to the scattered fields, via optimization. By using the spectral property of the current-to-field operator, the TSOM further shrinks the dimension of the current subspace within which the induced current is optimized. Since the new current subspace is much smaller than the one used in the SOM, the TSOM shows better stability and better robustness against noise compared the SOM. However, in order to obtain the spectral property of the current-to-field operator, the singular value decompostion (SVD) of the operator is involved, and it is computationally burdensome, especially when dealing with problems with a large amount of unknowns. In order to decrease the computational complexity, the FFT-TSOM is proposed. In the FFT-TSOM, the discrete Fourier bases are used to construct a current subspace that is a good approximation to the original current subspace spanned by singular vectors. Such an approximation avoids the SVD and uses the FFT to accomplish the construction of the induced current, which reduces the computational complexity and memory demand of the algorithm compared to the original TSOM. By using the new current subspace approximation, the FFT-TSOM inherits the merits of the TSOM, better stability during the inversion and better robustness against noise compared to the SOM, and meanwhile has much lower computational complexity than the TSOM. Numerical tests for both TSOM and FFT-TSOM will be shown in the seminar.