基于空间域压缩采样和谱域Karhunen-Loève变换的光谱成像与重构  

Spectral Imaging and Reconstruction Based on Spatial Compressive Sampling and Spectral Karhunen-Loève Transform

作　　者：唐意东[1] 黄树彩[1] 黄达 Tang Yidong;Huang Shucai;Huang Da(College of Air and Missile Defense, Air Force Engineering University, Xi＇an, Shaanxi 710051, China)

机构地区：[1]空军工程大学防空反导学院,陕西西安710051

出　　处：《光学学报》2018年第5期343-352,共10页Acta Optica Sinica

基　　金：国家自然科学基金(61273275)

摘　　要：光谱图像包含丰富的空间信息和光谱信息,能够为天基预警探测任务提供重要的信息支撑,但其庞大的数据量给硬件设备带来了极大的挑战。传统的基于奈奎斯特采样的"先采样后压缩"的处理方式不仅无法从根本上解决数据量庞大的问题,还会造成资源浪费;针对此问题,利用单波段二维图像的稀疏性和空间编码数据的谱间冗余,设计了一种基于空间域压缩采样和谱域Karhunen-Loève(KL)变换编码的光谱图像重构方法,并建立基于1范数和全变分约束的单波段二维图像复合正则重构模型,同时结合投影梯度法和软阈值收缩算子设计2D-CRPG模型求解算法。结果表明:基于空间域压缩采样和谱域KL变换编码的光谱图像重构方法能够有效降低数据采样成本,有利于天基预警探测光谱成像;2D-CRPG重构算法能够有效保留光谱图像的结构信息,从而在有限的采样率下较好地重构原始光谱图像。Spectral images contain abundant space information and spectral information,which can provide important information support for space-based early warning detection.However,the huge amounts of data also brings great challenge for hardware.The traditional treatment of first sampling and then compressing based on Nyquist sampling not only can＇t solve the problem of mass-data fundamentally,but also causes wasting of sources.To solve this problem,we propose a spectral imaging and reconstruction method based on spatial compressive sampling and spectral Karhunen-Loève（KL）transform by using the sparsity of single-band images and the spectral redundant of spatial encoded data.A two-dimensional composite regular reconstruction model based on l_1-norm and total variation is constructed for single band images,and an inference algorithm named two-dimensional compound regularized projection gradient（2 D-CRPG）is then proposed for the model by combining the projection gradient method with the soft-threshold operator.The results show that the spectral imaging and reconstruction method based on spatial compressive sampling and KL transform can effectively reduce the cost of data sampling,and thus can benefit the spectral imaging of space-based early warning detection.The 2 D-CRPG reconstruction algorithm can effectively preserve structural information of spectral images,thus the original spectral image can be reconstructed at a limited sampling rate.

关 键 词：光谱学 压缩感知 解码重构 Karhunen-Loève变换 稀疏表示 

分 类 号：TP751.1[自动化与计算机技术—检测技术与自动化装置]