Cross-sectional optoacoustic tomographic reconstructions in a polar grid

Some commonly employed optoacoustic (photoacoustic) tomographic configurations make use of an array of cylindrically-focused transducers located around the imaging sample to selectively acquire the optoacoustic signals generated in the imaging plane. Thereby, the feasibility of simultaneous acquisition of signals leads to important advantages such as high-throughput performance or real-time imaging capacity. For this particular geometry, two-dimensional model-based reconstruction has showcased good performance in terms of imaging accuracy and flexibility to account for various transducer-related effects and acoustic propagation phenomena. The forward model is expressed as a linear operator (model-matrix) that maps the optical absorption in a grid containing the sample to the resulting wavefield at the sensor positions. The standard approach, however, may lead to excessive memory requirements for the storage of the model-matrix. Herein, an optoacoustic model based on a discretization of the time-domain equation in a polar grid is introduced. Due to the rotational symmetry of the acquisition geometry and the discretization grid, only the part of the model-matrix directly corresponding to one transducer position (projection) needs to be stored. As a result, inversion of the model-matrix can be done in a memory efficient manner. Performance of the method was tested in numerical simulations and experimental measurements, attaining results equivalent to Cartesian-based grids but using a much more computationally efficient implementation.