Multi-Scale Factorization of the Wave Equation with Application to Compressed Sensing Photoacoustic Tomography
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By performing a large number of spatial measurements, high spatial resolution photoacoustic imaging can be achieved without specific prior information. However, the acquisition of spatial measurements is time consuming, costly and technically challenging. By exploiting non-linear prior information, compressed sensing techniques in combination with sophisticate reconstruction algorithms allow a reduction of number of measurements while maintaining a high spatial resolution. For this purpose, in this paper, we propose a multiscale factorization for the wave equation, which separates the data into a low frequency factor and sparse high frequency factors. By extending the acoustic reciprocal principle, we transfer sparsity in measurements domain to spatial sparsity of the initial pressure, which allows the use of sparse reconstruction techniques. Numerical results are presented which demonstrate the feasibility of the proposed framework.
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