平均采样与压缩采样及其在波浪监测中的应用研究

Irregular sampling has been being a hot theory in the community of signal processing and leads the development trend of research on signal processing. In the past 20 years, the local average sampling theory based on mathematical model accorded with the reality of compressed sampling and was recognized by the academic community. Currently, one-dimensional average sampling results are basically mature, and only a few of intractable problems are left. The common problems in high-dimensional average sampling have been solved, but main results are expected to be improved. Moreover, compressed sampling has received wide attention and become the hot theory all around the world with its extremely low sampling frequency and extraordinary high probabilistic reconstruction. RIP is a key factor in determining whether a signal can be compressed in the compressed sampling theory. RIP classification leads to the classification of the compressible signals, and reasonable classification on RIP will carve out a way for the wide applications of compressed sampling theory. So it is a very significant work to classify RIP by strict mathematic definition. The idea that we use the mathematical definitions to classify RIP has been approved by the international peers. Lastly, wave measurement algorithms based on navigation radar are very important to enhance China's ocean monitoring capacity and the level of wave forecasting. The applicant and his team have been working in exploratory experiments and related software development towards wave measurement by radar in the past six years, finding that compressed sampling theory is particularly suitable for the research of navigation radar echo signals. Therefore, this scientific research item combining mathematic and information engineering can have a profound impact on the economy and technology.

不规则采样理论多年来一直是信号处理领域的热点并引领信号处理领域的发展方向。近20年来，基于局部平均采样理论的数学模型以其更符合压缩采样实际而被学术界公认。目前平均采样的一维结果基本成熟，仅是遗留个别难点问题；高维结果一般问题也已经解决，主体高维结果有待完善。另外，从2006年起,压缩采样以其超低采样率、高概率重构的优良特点成为目前国际热点理论。其中RIP是信号可以进行压缩的关键，对RIP进行分类的结果是对可压缩信号进行分类，合理的分类会对压缩采样理论的广泛应用开辟道路。所以我们利用严格数学定义对RIP分类的设想得到国际同行认可。最后，基于导航雷达的测波算法对提升我国海洋监测能力和海浪预报水平也有重要意义。申请人及其团队近六年通过对雷达和浮标测波的探索性实验和相关软件开发，发现这类信号特别适合进行压缩采样应用研究。总之，本课题属于数学和信息紧密结合同时对经济技术能产生深远影响的课题。

不规则采样理论多年来一直是信号处理领域的热点并引领信号处理领域的发展方向。近20年来，基于局部平均采样理论的数学模型以其更符合压缩采样实际而被学术界公认。目前平均采样的一维结果基本成熟，仅是遗留个别难点问题；高维结果一般问题也已经解决，主体高维结果有待完善。另外，从2006年起,压缩采样以其超低采样率、高概率重构的优良特点成为目前国际热点理论。其中RIP是信号可以进行压缩的关键，对RIP进行分类的结果是对可压缩信号进行分类，合理的分类会对压缩采样理论的广泛应用开辟道路。 最后，基于导航雷达的测波算法对提升我国海洋监测能力和海浪预报水平也有重要意义。我们通过对X波段雷达测波的探索性实验实现相关软件开发。