一种基于压缩感知理论的LCTF光谱超分辨方法

液晶可调谐滤光片（LCTF）因其在宽谱段上具有简单、高效的调谐滤光功能常作为微型光谱仪应用在多种测量领域.然而,滤光式光谱仪的光谱分辨能力受限于其系统的带宽,进行高分辨测量时的硬件成本和测量数据量都较大.将压缩感知理论引入LCTF的光谱测量中,通过将LCTF获取的测量数据与其对应的调谐波长处的透过率函数进行关联计算,得到光谱分辨率优于系统带宽的目标光谱曲线.分析表明,本文模型下的压缩感知测量矩阵具有良好的非相关性,同时对地物光谱进行的压缩感知重构结果表明,在仅进行32次测量的条件下,本文方法得到了珍珠石目标的128波段的光谱曲线,能分辨出传统方法不能分辨的光谱细节,且反射率的平均误差仅有0.75%,同时对噪声具有一定的抵抗性. 

A Spectral Super-Resolution Method of LCTF Based on Compressive Sensing

The liquid crystal tunable filter (LCTF) is used as micro spectrometer in many measuring fields for its simple and efficient light filter function. But the spectral resolution of LCTF is limited by its bandwidth, and the hardware cost and larger measure data are the problem in higher resolution measuring. In this paper, combining the compressive sensing with the LCTF spectral measuring method, a new model was proposed to get the object spectral curve with a superior spectral resolution than the system bandwidth. In the model, the data calculation of LCTF spectral measurement was correlated with its transmittance function of corresponding wavelength. Analysis results show that, the measurement matrix in the proposed model possesses a good incoherence property. The simulation results of real earth object''s spectrum show that, the spectral curve of 128 band pearl stone can be reconstructed with only 32 measurements, the mean error of reflectance is only 0.75% with a certain noise repellency, and the spectral details can be distinguished while traditional method cannot work.