In this talk, I will describe how the theory of nonuniform Fourier frames may be applied to the reconstruction problem in photoacoustic tomography (PAT). PAT is a novel medical imaging modality coupling laser pulses with ultrasounds, allowing for measuring the high-contrast optical parameters of tissues by means of high-resolution ultrasonic measurements. Compressed sensing (CS) PAT has been largely studied over the last years, but without rigorous theoretical guarantees. In this talk, I will discuss how the theory of Riesz sequences of exponentials allows us to reduce the problem of CS PAT to classical CS for undersampled Fourier measurements. This is a joint work with Paolo Campodonico and Matteo Santacesaria.