基于压缩感知与分段 Hermite 插值的二维温度场重构方法

在遥感测绘、爆炸场测试和物流安全等领域，往往需要高精度测量二维温度场信息。由于测量面积较大或者监测设备有限，经常导致温度场测试精度和分辨率较低。为此，本文结合压缩感知与分段Hermite插值理论提出一种二维温度场压缩重构方法。该方法首先对温度场进行随机欠采样；然后对采样结果进行分段Hermite插值以提高采样率；最后利用插值结果进行OMP高概率重构。该方法可以有效降低二维温度场测试的测量点数量。试验表明，在压缩率为75%情况下，二维温度场的重建误差不大于6.5%。

Two-dimensional temperature field reconstruction method based oncompressed sensing and piecewise Hermite interpolation

In the fields of remote sensing mapping, explosion field testing and logistics security, it is often necessary to measure twodimensional temperature field information with high precision. Due to the large measurement area or limited monitoring equipment,temperature field measurement accuracy and resolution are often low. Therefore, this paper proposes a two-dimensional temperature fieldcompression and reconstruction method combining compressive sensing and piecewise Hermite interpolation theory. Firstly, thetemperature field is undersampled randomly. Secondly, the sampling results are interpolated by Hermite interpolation to improve thesampling rate. Finally, the interpolation results are used to reconstruct by OMP with high probability. This method can effectively reducethe number of measuring points in two-dimensional temperature field measurement. The experimental results indicate that thereconstruction error of two-dimensional temperature field is no more than 6. 5% when the compression rate is 75%.