Quantitative photoacoustic tomography with piecewise constant material parameters

The goal of quantitative photoacoustic tomography is to determine optical and acoustical material properties from initial pressure maps as obtained, for instance, from photoacoustic imaging. The most relevant parameters are absorption, diffusion and Grueneisen coefficients, all of which can be heterogeneous. Recent work by Bal and Ren shows that in general, unique reconstruction of all three parameters is impossible, even if multiple measurements of the initial pressure (corresponding to different laser excitation directions at a single wavelength) are available. Here, we propose a restriction to piecewise constant material parameters. We show that in the diffusion approximation of light transfer, piecewise constant absorption, diffusion and Gr\"uneisen coefficients can be recovered uniquely from photoacoustic measurements at a single wavelength. In addition, we implemented our ideas numerically and tested them on simulated three-dimensional data

A variational method for quantitative photoacoustic tomography with piecewise constant coefficients

In this article, we consider the inverse problem of determining spatially heterogeneous absorption and diffusion coefficients from a single measurement of the absorbed energy (in the steady-state diffusion approximation of light transfer). This problem, which is central in quantitative photoacoustic tomography, is in general ill-posed since it admits an infinite number of solution pairs. We show that when the coefficients are known to be piecewise constant functions, a unique solution can be obtained. For the numerical determination of the coefficients, we suggest a variational method based based on an Ambrosio-Tortorelli-approximation of a Mumford-Shah-like functional, which we implemented numerically and tested on simulated two-dimensional data

ERK1/2 MAP kinases promote cell cycle entry by rapid, kinase-independent disruption of retinoblastoma–lamin A complexes

When in the nucleus, ERK1/2 dislodges the retinoblastoma protein from lamin A, facilitating its rapid phosphorylation