Abstract Within the compressive sensing (CS) framework, one effective way to increase the likelihood of successful signal reconstruction is to employ random processes in the construction of the sensing matrix. This study presents a 3D holey cavity, with diverse frequency modes, to spectrally code, that is, randomize, the ultrasound wave fields. The simulated results show that the use of such a cavity enables imaging simple or complex targets, such as spheres or the letter E, by only a single transceiver—something that is not possible without the use of a coding structure like the cavity. The effect of noise on imaging results and the size of the targets on the first-order Born approximation (BA) are also investigated. Moreover, this study attempts to optimize the cavity, based on a single numerical metric, such as the sum of singular values (SSV) or mutual coherence (MC). Yet, it will be shown that neither of these metrics can consistently compare the norm-one imaging performance between two cavities of different materials or hole sizes. This leaves finding a quantitative metric for these kinds of optimizations an open problem.

中文翻译：

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具有物理优化的用于单换能器 3D 超声成像的空腔

摘要 在压缩感知 (CS) 框架内，增加成功信号重建可能性的一种有效方法是在感知矩阵的构建中采用随机过程。这项研究提出了一个具有不同频率模式的 3D 多孔腔，可以对超声波场进行频谱编码，即随机化。模拟结果表明，使用这种空腔可以仅通过单个收发器对简单或复杂的目标（例如球体或字母 E）进行成像——如果不使用像空腔这样的编码结构，这是不可能实现的。还研究了噪声对成像结果的影响以及目标大小对一阶 Born 近似 (BA) 的影响。此外，本研究尝试基于单个数值度量优化腔体，例如奇异值总和 (SSV) 或相互相干 (MC)。然而，将表明这些指标都不能始终如一地比较不同材料或孔尺寸的两个腔体之间的标准一成像性能。这使得为​​这些类型的优化寻找量化指标成为一个悬而未决的问题。