Haltmeier Markus, Sandbichler Michael, Berer Thomas, Bauer-Marschallinger Johannes, Burgholzer Peter, Nguyen Linh
Department of Mathematics, University of Innsbruck, Technikestraße 13, Innsbruck, 6020, Austria.
Research Center for Non-Destructive Testing (RECENDT), Altenberger Straße 69, Linz, 4040, Austria.
J Acoust Soc Am. 2018 Jun;143(6):3838. doi: 10.1121/1.5042230.
Compressed sensing (CS) is a promising approach to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. This allows to increase the measurement speed and reduce system costs. Instead of collecting point-wise measurements, in CS one uses various combinations of pressure values at different sensor locations. Sparsity is the main condition allowing to recover the photoacoustic (PA) source from compressive measurements. In this paper, a different concept enabling sparse recovery in CS PAT is introduced. This approach is based on the fact that the second time derivative applied to the measured pressure data corresponds to the application of the Laplacian to the original PA source. As typical PA sources consist of smooth parts and singularities along interfaces, the Laplacian of the source is sparse (or at least compressible). To efficiently exploit the induced sparsity, a reconstruction framework is developed to jointly recover the initial and modified sparse sources. Reconstruction results with simulated as well as experimental data are given.
压缩感知（CS）是一种很有前景的方法，可在保持高空间分辨率的同时减少光声断层扫描（PAT）中的测量次数。这有助于提高测量速度并降低系统成本。在CS中，不是逐点收集测量值，而是使用不同传感器位置处压力值的各种组合。稀疏性是从压缩测量中恢复光声（PA）源的主要条件。本文介绍了一种在CS PAT中实现稀疏恢复的不同概念。该方法基于这样一个事实，即应用于测量压力数据的二阶时间导数相当于对原始PA源应用拉普拉斯算子。由于典型的PA源由沿界面的平滑部分和奇点组成，源的拉普拉斯算子是稀疏的（或至少是可压缩的）。为了有效地利用诱导的稀疏性，开发了一个重建框架来联合恢复初始和修改后的稀疏源。给出了模拟数据和实验数据的重建结果。
