利用正交匹配追踪算法对高光谱图像进行压缩感知重构,是通过寻找最优原子对原始信号进行线性表示,使残差不断减小以获取重构信号。在处理基于冗余字典的重构问题时,其耗时主要存在于原子匹配过程和残差更新过程,导致算法的计算复杂度较高、难以实现实时处理。针对此缺陷,提出一种用于高光谱图像的埃尔米特压缩感知重构算法,主要思想是:利用埃尔米特求逆引理,对正交匹配追踪算法残差更新的迭代过程进行优化;进一步地,采用人工鱼群算法寻找最优原子,对匹配过程进行加速,以提高执行效率。利用所提算法对高光谱图像进行压缩感知重构处理,合理设置算法参数,在保证重构精度的条件下,与正交匹配追踪算法相比,所提算法能将计算速度提高10倍左右。

Utilizing orthogonal matching pursuit algorithm for compressed sensing reconstruction of hyperspectral images is to find the optimal atoms to linearly represent the original signal, so that the residual is continuously reduced to obtain the reconstructed signal. When dealing with the redundant dictionary-based reconstruction, the time consuming mainly exists in its atom matching process and residual updating process, resulting in high computational complexity and difficulty of real-time processing. Aiming at this defect, a Hermitian compressed sensing reconstruction algorithm for hyperspectral images is proposed. The main idea is Hermitian inversion lemma is used to optimize the iterative process of the residual update to improve the execution efficiency of the algorithm. In addition, the artificial fish swarm algorithm is used to find the optimal atoms and accelerate the matching process to further improve the reconstruction efficiency. The experimental results carried out on hyperspectral images show that the computational efficiency of the proposed algorithm can be improved by about 10 times compared with the traditional orthogonal matching pursuit algorithm under the condition of ensuring the reconstruction accuracy.