SIAM Journal on Imaging Sciences, Volume 14, Issue 3, Page 1039-1077, January 2021.
Photoacoustic tomography (PAT) is an emerging imaging modality that aims at measuring the high-contrast optical properties of tissues by means of high-resolution ultrasonic measurements. The interaction between these two types of waves is based on the thermoacoustic effect. In recent years, many works have investigated the applicability of compressed sensing to PAT in order to reduce measuring times while maintaining a high reconstruction quality. However, in most cases, theoretical guarantees are missing. In this work, we show that in many measurement setups of practical interest, compressed sensing PAT reduces to compressed sensing for undersampled Fourier measurements. This is achieved by applying known reconstruction formulae in the case of the free-space model for wave propagation, and by applying the theories of Riesz bases and nonuniform Fourier series in the case of the bounded domain model. Extensive numerical simulations illustrate and validate the approach.

中文翻译：

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压缩传感光声层析成像减少到压缩传感用于欠采样傅立叶测量

SIAM 成像科学杂志，第 14 卷，第 3 期，第 1039-1077 页，2021 年 1 月。
光声断层扫描 (PAT) 是一种新兴的成像方式，旨在通过高分辨率超声测量来测量组织的高对比度光学特性。这两种类型的波之间的相互作用基于热声效应。近年来，许多工作研究了压缩感知对 PAT 的适用性，以减少测量时间，同时保持较高的重建质量。但是，在大多数情况下，缺少理论上的保证。在这项工作中，我们展示了在许多具有实际意义的测量设置中，压缩感知 PAT 简化为用于欠采样傅立叶测量的压缩感知。这是通过在波传播的自由空间模型的情况下应用已知的重建公式来实现的，并通过在有界域模型的情况下应用 Riesz 基和非均匀傅立叶级数的理论。广泛的数值模拟说明并验证了该方法。