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Performing a large number of spatial measurements enables high-resolutionphotoacoustic imaging without specific prior information. However, theacquisition of spatial measurements is time-consuming, costly, and technicallychallenging. By exploiting nonlinear prior information, compressed sensingtechniques in combination with sophisticated reconstruction algorithms allowreducing the number of measurements while maintaining high spatial resolution.To this end, in this work we propose a multiscale factorization for the waveequation that decomposes the measured data into a low-frequency factor andsparse high-frequency factors. By extending the acoustic reciprocity principle,we transfer sparsity in the measurement domain into spatial sparsity of theinitial pressure, which allows the use of sparse reconstruction techniques.Numerical results are presented that demonstrate the feasibility of theproposed framework.

Multi-Scale Factorization of the Wave Equation with Application to Compressed Sensing Photoacoustic Tomography