  Performing a large number of spatial measurements enables high-resolution
photoacoustic imaging without specific prior information. However, the
acquisition of spatial measurements is time-consuming, costly, and technically
challenging. By exploiting nonlinear prior information, compressed sensing
techniques in combination with sophisticated reconstruction algorithms allow
reducing the number of measurements while maintaining high spatial resolution.
To this end, in this work we propose a multiscale factorization for the wave
equation that decomposes the measured data into a low-frequency factor and
sparse high-frequency factors. By extending the acoustic reciprocity principle,
we transfer sparsity in the measurement domain into spatial sparsity of the
initial pressure, which allows the use of sparse reconstruction techniques.
Numerical results are presented that demonstrate the feasibility of the
proposed framework.
