ABSTRACT
Developing reconstruction methods in photoacoustic or thermoacoustic tomography (PAT or TAT) has been a craftwork. This chapter applies time-reversal methods to derive exact and approximate reconstruction algorithms for PAT or TAT in an arbitrary configuration for the first time. It shows that the energy deposition in TAT is equivalent to the initial pressure distribution. The chapter introduces some basic concepts of time reversal, an exact time-reversal formula, and an approximate one in the form of delay-and-sum. It presents a reconstruction formula in TAT by time reversing the acoustic field to the time when the to-be-reconstructed point is excited. The reconstruction algorithm is verified by a numerical simulation of 3-D TAT. The reconstruction in TAT is equivalent to reverting the pressure field to time zero. This concept can also be adopted to derive the TAT reconstruction algorithm in a known acoustically heterogeneous medium.
