Photoacoustic ToF tomography of blood cells: From mathematical approximation to super-resolution

Photoacoustic or PA waves, generated from blood cells, create distinct spectral features in the Fourier domain, for example, maxima and minima. In this way, high-frequency PA signals can be used to identify and distinguish blood cells. However, due to finite bandwidth of physical systems, many interesting Fourier features are invisible within the observed bandwidth. To overcome this challenge, we reformulate the PA imaging problem as a time-of-flight super-resolution problem. Based on the PA wave equations, we show that the problem reduces to estimation of sparse cellular features from a set of finite trigonometric moments. For this purpose, we develop a super-resolution algorithm which achieves near exact performance (in context of maximum likelihood estimation) when working with experimental data. Hence, our work alleviates an important bottleneck in PA imaging linked with classification of cellular features.