A dynamic state estimator for photoacoustic reconstruction

Abstract The photoacoustic (PA) effect is an emerging technique for characterizing the structural and compositional features of materials by combining light absorption with the generation of pressure waves. In practice, it is only possible to measure the pressure wave at the sample surface using an ultrasound transducer, namely a PA signal. However, reconstructing the initial pressure is an inverse problem with a non-trivial solution. This work introduces a dynamic state estimator (DSE) that virtually measures wave propagation to compute the initial pressure profile from boundary measurements. The proposal is based on a dynamical model that describes the spatiotemporal evolution of a PA signal, where the states represent the pressure waves within the sample. Through the DSE, the method provides a smooth reconstruction of the initial pressure in a straightforward yet robust manner. The state estimator is tested in both numerical and real experiments, outperforming traditional model-based algorithms and yielding results comparable to the well-known time-reversal algorithm in signal-to-noise ratio, contrast, and computational speed. The results suggest that the state estimator represents a technological advancement in overcoming the inherent ill-posedness of the PA inverse problem in a wide range of applications.