Abstract We explore the effect of sampling rates when measuring data given by Mf for special operators M arising in Thermoacoustic Tomography. We start with sampling requirements on Mf given f satisfying certain conditions. After this we discuss the resolution limit on f posed by the sampling rate of Mf without assuming any conditions on these sampling rates. Next we discuss aliasing artifacts when Mf is known to be under sampled in one or more of its variables. Finally, we discuss averaging of measurement data and resulting aliasing and artifacts, along with a scheme for anti-aliasing.

中文翻译：

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热声断层扫描中的采样

摘要 我们探讨了在测量由 Mf 给出的数据时采样率的影响，该数据用于热声层析成像中出现的特殊算子 M。我们从满足特定条件的 f 对 Mf 的采样要求开始。在此之后，我们讨论了 Mf 的采样率对 f 的分辨率限制，而不假设这些采样率的任何条件。接下来我们讨论当已知 Mf 在其一个或多个变量中采样不足时的混叠伪影。最后，我们讨论了测量数据的平均和由此产生的混叠和伪影，以及抗混叠方案。