ABSTRACT

Photoacoustic tomography (PAT) is a recently developed imaging technique. It is based on the photoacoustic effect, andit has a big promise of successful applications for various biomedical tasks. For example, for tumor angiogenesis monitoring, blood oxygenation mapping, functional brain imaging, skin melanoma detection.

When short pulses of non-ionising electromagnetic energy are delivered into a bio- logical (semitransparent) tissue, then parts of the electromagnetic energy become absorbed. The absorbed energy leads to a nonuniform thermoelastic expansion (de- pending on the tissue structure), which in turn generates ultrasonic waves. These waves are detected by a measurement device on the boundary of the tissue. The mathematical task in PATis to reconstruct the spatially varying absorption coeffi- cient using these measurements. The values of the absorption coefficient inside the tissue allow to make a judgment about the directly unseen structure of the tissue. For example, whether there are some abnormal formations insidetheinvestigatedtissue, suchasatumor.

In practice,theboundaryofthetissueisoftennotfullyaccessible,whichleadstothe so-calledlimitedview problem (LVP). This case makes additional complications for the reconstruction of the absorption coefficient. Therefore, the development of the appropriate mathematical methods for this case is of big scientific interest.

In this talk, we propose a conceptually new perspective on the LVP. Namely, we propose a learning scheme that constructs anestimationoftheoperator thatmaps the data from the accessible part ofthe boundary to the data on the inaccessible part. This operator allows a transformation of the LVPto the fullviewproblemthat is easier tosolve.

The talk is based on the results of the joint work with Markus Haltmeier (Depart- ment of Mathematics, University of Innsbruck, Austria) and Vera Kurkova (Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague). This research is supported by the Tyrolean Science Fund.