脉冲流新息率采样及其在超声成像中的应用
Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging
摘要：
由短脉冲流组成的信号出现在许多应用中，包括生物成像和雷达。最近的有限创新率框架已经为这种脉冲的低速率采样铺平了道路，注意到每单位时间只需要少量的参数来完全描述这些信号。不幸的是，对于高创新率，现有的抽样方案是数值不稳定的。在本文中，我们提出了一个通用的采样方法，导致稳定的恢复，即使在存在许多脉冲。我们首先推导出一个条件的采样内核，它允许完美的重建周期性流从最小数量的样本。然后，我们设计了一个紧支撑类的过滤器，满足这个条件。的周期性解决方案扩展到有限和无限流，并示出了数值稳定，即使对于大量的脉冲。高噪声鲁棒性也表现出充分分离的延迟时。最后，我们使用我们的技术处理超声成像数据，并表明相对于传统的超声采样方案，可以实现大幅降低速率。
英文摘要：
Signals comprised of a stream of short pulses appear in many applications including bio-imaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing sampling schemes are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams from the minimal number of samples. We then design a compactly supported class of filters, satisfying this condition. The periodic solution is extended to finite and infinite streams, and is shown to be numerically stable even for a large number of pulses. High noise robustness is also demonstrated when the delays are sufficiently separated. Finally, we process ultrasound imaging data using our techniques, and show that substantial rate reduction with respect to traditional ultrasound sampling schemes can be achieved.
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