In this work, we suggest new spatial precipitation interpolation schemes using compressed sensing (CS), which is a new framework for signal acquisition and smart sensor design. Using CS, the precipitation maps are recovered in high resolution by obtaining sparse coefficients of radial basis functions(RBFs). Two types of methods are designed according to the construction methods of CS matrix. In the first type, the CS matrix is derived as the product of an m × n (n ≫ m) weights matrix of inverse distance weighting (IDW) and an n × n radial basis function (RBF) matrix. The second type of CS matrix consists of an m × n RBF matrix that depends on a few observation vectors and a number of n unknown vectors. The advantage of the proposed CS methods is that it can be represented at a high resolution because it is interpolated based on a large number of bases (or degrees of freedom). This prevents the variance value from being much smaller than the actual value due to interpolation using a few observation scales. To test our CS interpolation schemes, interpolation results were compared with IDW, Ordinary Kriging (OK) and RBF interpolation methods for analytic test function and some actual rainfall data. In the case of an analytic test function, when the proposed method is compared at high resolution, the error from the true value is the smallest. In real rainfall data, comparison with real values is not possible at high resolutions, but the error with the observed data is the smallest in terms of ‘spatial variogram’. In addition, the proposed CS method generates hight resolution data from rainfall cases, showing promising results when identifying peaks.

在这项工作中，我们建议使用压缩传感（CS）的新的空间降水插值方案，这是用于信号采集和智能传感器设计的新框架。使用CS，通过获取径向基函数（RBF）的稀疏系数，可以高分辨率恢复降水图。根据CS矩阵的构造方法设计了两种方法。在第一种类型中，CS矩阵推导的产物米× Ñ（Ñ »米）反距离加权（IDW）的权重矩阵和Ñ × Ñ径向基函数（RBF）的矩阵。第二类CS矩阵由m × nRBF矩阵取决于一些观测向量和n个未知向量。所提出的CS方法的优点是，由于它是基于大量基数（或自由度）进行插值的，因此可以高分辨率显示。这可以防止由于使用少量观察标度进行插值而使方差值比实际值小得多。为了测试我们的CS插值方案，将插值结果与IDW，普通Kriging（OK）和RBF插值方法进行了比较，以用于分析测试功能和一些实际降雨数据。在分析测试功能的情况下，在高分辨率下比较提出的方法时，来自真实值的误差最小。在真实降雨数据中，无法在高分辨率下与真实值进行比较，但是就“空间变异图”而言，观测数据的误差最小。此外，