Acoustic attenuation describes the loss of energies of propagating waves. This effect is inherently frequency dependent. Typical attenuation models are derived phenomenologically and experimentally without the use of conservation principles. Because of these general strategy a zoo of models has been developed over decades.

Photoacoustic imaging is a hybrid imaging technique where the object of interest is excited by a laser and the acoustic response of the medium is measured outside of the object. From this the ability of the medium to convert laser excitation into acoustic waves is computationally reconstructed. For photoacoustics, which is a linear inverse problem, we will determine its spectral values, and we shall see that there are two kind of attenuating models, resulting in mildly and severely inverse photoacoustic problems.

Coupled Physics Imaging methods combine image contrast from one physical process with observations using a secondary process; several modalities in acousto-optical imaging follow this concept wherein optical contrast is observed with acoustic measurements. For the inverse problem both an optical and acoustic model need to be inverted. Classical methods that involve a non-linear optimisation approach can be combined with advances in stochastic subsamplings strategies that are in part inspired by machine learning applications. In such approaches the forward problem is considered deterministic and the stochasticity involves splitting of an objective function into sub functions that approach the fully sampled problem in an expectation sense.

In this work we consider where the forward problem is also solved stochastically, by a Monte Carlo simulation of photon propagation. By adjusting the batch size in the forward and inverse problems together, we can achieve better performance than if subsampling is performed seperately.

Joint work with : S. Powell, C. Macdonald, N. Hänninen, A. Pulkkinen, T. Tarvainen

Range invariance is a property that - like the tangential cone condition - enables a proof of convergence of iterative methods for inverse problems. In contrast to the tangential cone condition it can also be verified for some parameter identification problems in partial differential equations PDEs from boundary measurements, as relevant, e.g., in tomographic applications. The goal of this talk is to highlight some of these examples of coefficient identification from boundary observations in elliptic and parabolic PDEs, among them: combined diffusion and absorption identification (e.g., in steady-state diffuse optical tomography), reconstruction of a boundary coefficient (e.g. in corrosion detection), reconstruction of a coefficient in a quasilinear wave equation (for nonlinearity coefficient imaging).

During the last three decades, the new field of mechanobiology has demonstrated that mechanical forces play a key role for the decision making of biological cells. The standard way to estimate cell forces is traction force microscopy on soft elastic substrates, whose deformations can be tracked with fiducial marker beads. To infer the corresponding cell forces, one can either solve the inverse problem of elasticity, which usually is done in Fourier space, or calculate strain and stress tensors directly from the deformation data. In both cases, some type of regularization is required to deal with experimental noise. Here we discuss recent developments in this field, including microparticle traction force microscopy and machine learning approaches.