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Photoacoustic (PA) imaging combines optical excitation with ultrasonic detection to achieve high-resolution imaging of biological samples. A high-energy pulsed laser is often used for imaging at multi-centimeter depths in tissue. These lasers typically have a low pulse repetition rate, so to acquire images in real-time, only one pulse of the laser can be used per image. This single pulse necessitates the use of many individual detectors and receive electronics to adequately record the resulting acoustic waves and form an image. Such requirements make many PA imaging systems both costly and complex. This investigation proposes and models a method of volumetric PA imaging using a state-of-the-art compressed sensing approach to achieve real-time acquisition of the initial pressure distribution (IPD) at a reduced level of cost and complexity. In particular, a single exposure of an optical image sensor is used to capture an entire Fabry–Pérot interferometric acoustic sensor. Time resolved encoding as achieved through spatial sweeping with a galvanometer. This optical system further makes use of a random binary mask to set a predetermined subset of pixels to zero, thus enabling recovery of the time-resolved signals. The Two-Step Iterative Shrinking and Thresholding algorithm is used to reconstruct the IPD, harnessing the sparsity naturally occurring in the IPD as well as the additional structure provided by the binary mask. We conduct experiments on simulated data and analyze the performance of our new approach.