论文标题
压缩感测光声层析成像可减少到压缩感应的傅立叶测量
Compressed sensing photoacoustic tomography reduces to compressed sensing for undersampled Fourier measurements
论文作者
论文摘要
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测量组织的高对比度光学特性。这两种波浪之间的相互作用是基于热声效应。近年来，许多工作调查了压缩传感对PAT的适用性，以减少测量时间，同时保持高重建质量。但是，在大多数情况下，缺少理论保证。在这项工作中，我们表明，在许多实践兴趣的测量设置中，压缩感应的PAT降低至压缩感测，以进行不足的傅立叶测量。这是通过在自由空间模型的情况下应用已知的重建公式来实现的，并在有界域模型的情况下应用Riesz碱基和非均匀傅立叶序列的理论。广泛的数值模拟说明并验证方法。
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.
