In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation of sparse sensing. It is different from compressed sensing, which exploits the sparse representation of a signal to reduce sample complexity (compressed sampling or acquisition). We use sparse sensing to denote a board concept of methods whose main focus is to improve the efficiency and cost of sampling implementation itself. The "sparse" here is referred to sampling at a low temporal or spatial rate (sparsity constrained sampling or acquisition), which in practice models cheaper hardware such as lower power, less memory and throughput. We take frequency and direction of arrival (DoA) estimation as concrete examples and give the necessary and sufficient requirements of the sampling strategy. Interestingly, we prove that these problems can be reduced to some (multiple) remainder model. As a straightforward corollary, we supplement and complete the theory of co-prime sampling, which receives considerable attention over last decade. On the other hand, we advance the understanding of the robust multiple remainder problem, which models the case when sampling with noise. A sharpened tradeoff between the parameter dynamic range and the error bound is derived. We prove that, for N-frequency estimation in either complex or real waveforms, once the least common multiple (lcm) of the sampling rates selected is sufficiently large, one may approach an error tolerance bound independent of N.
翻译:在系列文件的第一部分,我们提出回答下列问题:鉴于对一组取样员的具体限制,什么信号可以作为稀有感测的基础,以获得的相应样品作为稀有感应的基础,而具有独特性的信号,与压缩感测不同,因为压缩感测利用一个信号的稀少表示来降低抽样复杂性(压缩取样或获取);我们使用稀疏感来表示一种委员会方法概念,其主要重点是提高采样实施本身的效率和成本。这里提到的“稀有性”是指低时间或空间采样率(不同采样或获取)的采样,这种采样实际上以较低的功率、较少的内存和吞吐量等较便宜的硬件为模型。我们把到货的频率和方向作为具体例子,并给出取样战略的必要和充分要求。有趣的是,我们证明这些问题可以降为某些(多倍)剩余采样模型。作为一个直截然的必然结果,我们补充并完成共同初采样的理论,这在过去十年里引起了相当大的注意。另一方面,我们增进了对一个坚固的余问题的理解,即当我们用一个常规的模型来测算时,在一种动态的测算中,在一种测算中,一种测算的测算中,我们可能的测得的测得的测算为一种测得的测得的测得的比。