基于改进MCA的干涉高光谱图像分解

干涉高光谱图像特殊的成像原理，使其帧内存在着大幅值且位置固定的干涉条纹，而帧间存在着水平移位的背景图像，这种特点会严重的破坏原始图像的固有结构，从而导致新兴的压缩感知理论与传统压缩算法的直接应用无法得到理想的效果。由于干涉条纹信息与背景图像信息的特征不同，能够对干涉条纹与背景图像进行稀疏表示的正交基也是不同的。基于这种思想，使用MCA(morphological component analysis)算法对干涉高光谱图像中干涉条纹信息与背景图像信息进行分离处理。由于干涉高光谱图像数据量庞大，传统的MCA算法对干涉高光谱数据的图像分解，迭代收敛速度慢，运算效率较低，故而针对干涉高光谱数据特点对传统MCA算法进行改进，改变其迭代收敛条件，当分离后的图像信号与原始图像信号的误差已经基本保持不变时，即终止迭代;并根据对应正交基能且仅能稀疏表示对应信号的思想，对阈值采用自适应的方式进行更新，在新的阈值更新模式中，图像信号在不同正交基下的映射系数被计算与比较。大量实验结果表明，对于LASIS数据与LAMIS数据，MCA算法都能够较完美的将干涉高光谱图像分解，改进的MCA算法更能在保持完美分解输出结果的同时，相对于传统MCA方法显著的减小迭代次数，更快的达到迭代收敛条件，从而有效的提高了算法的运算效率与实时性需求，也为新兴的压缩感知理论在干涉高光谱图像中的进一步应用提供了一种很好的解决方案。

Decomposition of Interference Hyperspectral Images Using Improved Morphological Component Analysis

As the special imaging principle of the interference hyperspectral image data ,there are lots of vertical interference stripes in every frames .The stripes’ positions are fixed ,and their pixel values are very high .Horizontal displacements also exist in the background between the frames .This special characteristics will destroy the regular structure of the original interference hyperspectral image data ,which will also lead to the direct application of compressive sensing theory and traditional compression algorithms can’t get the ideal effect .As the interference stripes signals and the background signals have different characteristics themselves ,the orthogonal bases which can sparse represent them will also be different .According to this thought ,in this paper the morphological component analysis (MCA) is adopted to separate the interference stripes signals and background signals .As the huge amount of interference hyperspectral image will lead to slow iterative convergence speed and low computational efficien‐cy of the traditional MCA algorithm ,an improved MCA algorithm is also proposed according to the characteristics of the inter‐ference hyperspectral image data ,the conditions of iterative convergence is improved ,the iteration will be terminated when the error of the separated image signals and the original image signals are almost unchanged .And according to the thought that the orthogonal basis can sparse represent the corresponding signals but cannot sparse represent other signals ,an adaptive update mode of the threshold is also proposed in order to accelerate the computational speed of the traditional MCA algorithm ,in the proposed algorithm ,the projected coefficients of image signals at the different orthogonal bases are calculated and compared in order to get the minimum value and the maximum value of threshold ,and the average value of them is chosen as an optimal threshold value for the adaptive update mode .The experimental results prove that whether LASIS and LAMIS image data ,the traditional MCA algorithm can separate the interference stripes signals and background signals very well ,and make the interfer‐ence hyperspectral image decomposition perfectly ,and the improved MCA algorithm not only keep the perfect results of the tra‐ditional MCA algorithm ,but also can reduce the times of iteration and meet the iterative convergence conditions much faster than the traditional MCA algorithm ,which will also provide a very good solution for the new theory of compressive sensing .