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.
We investigated a new optical approach for the detection of the coagulation dynamic process by means of the information on the optical vortex. In our study, laser speckle was captured using a high-speed CMOS camera, and the statistical information of
the optical vortex characterized the change in coagulation properties with time. Similar to the scattering particles, the motion of the optical vortex is restricted during coagulation, as a result, the whole process of coagulation can be detected by calculating the mean square displacement(MSD) of the optical vortex. The results demonstrate a close correlation between coagulation parameters measured using the optical vortex method and thrombelastography(TEG), creating a powerful opportunity for self-testing and real-time detection of coagulation.
