SIAM Journal on Imaging Sciences, Volume 14, Issue 2, Page 558-579, January 2021.
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.

中文翻译：

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波动方程的多尺度分解及其在压缩传感光声层析成像中的应用

SIAM影像科学杂志，第14卷，第2期，第558-579页，2021年1月。
执行大量空间测量可以实现高分辨率光声成像，而无需特定的先验信息。然而，空间测量的获取是费时，昂贵且在技术上具有挑战性的。通过利用非线性先验信息，压缩传感技术与复杂的重建算法相结合，可以在保持高空间分辨率的同时减少测量次数。为此，在这项工作中，我们为波动方程提出了多尺度分解，将测量数据分解为低频因子和稀疏高频因子。通过扩展声学互易原理，我们将测量域中的稀疏度转换为初始压力的空间稀疏度，从而允许使用稀疏重建技术。