论文标题
波动方程的多尺度分解，并应用于压缩传感光声断层扫描
Multi-Scale Factorization of the Wave Equation with Application to Compressed Sensing Photoacoustic Tomography
论文作者
论文摘要
进行大量空间测量可以实现高分辨率的光声成像，而无需具体的事先信息。但是，对空间测量的获取是耗时，昂贵且在技术上具有挑战性的。通过利用非线性先验信息，压缩感测技术与复杂的重建算法结合使用，可以减少测量数量，同时保持高空间分辨率。为此，在这项工作中，我们提出了波动方程的多尺度分解，将测量数据分解为低频因子和稀疏的高频因素。通过扩展声学互惠原理，我们将测量域中的稀疏性转移到初始压力的空间稀疏度中，从而允许使用稀疏的重建技术。提出了数字结果，以证明所提出的框架的可行性。
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.
