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Photoacoustic tomography (PAT) is an emerging imaging modality that aims atmeasuring the high-contrast optical properties of tissues by means ofhigh-resolution ultrasonic measurements. The interaction between these twotypes of waves is based on the thermoacoustic effect. In recent years, manyworks have investigated the applicability of compressed sensing to PAT, inorder to reduce measuring times while maintaining a high reconstructionquality. However, in most cases, theoretical guarantees are missing. In thiswork, we show that in many measurement setups of practical interest, compressedsensing PAT reduces to compressed sensing for undersampled Fouriermeasurements. This is achieved by applying known reconstruction formulae in thecase of the free-space model for wave propagation, and by applying the theoriesof Riesz bases and nonuniform Fourier series in the case of the bounded domainmodel. Extensive numerical simulations illustrate and validate the approach.

Compressed sensing photoacoustic tomography reduces to compressed sensing for undersampled Fourier measurements