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针对目前多光谱图像去马赛克算法存在计算量大、效率低的缺点，本文提出一种基于压缩感知的多光谱图像去马赛克算法。首先，分析去马赛克与压缩感知问题的等价性，建立基于压缩感知的去马赛克模型；然后，采用离散余弦变换构建压缩感知的稀疏基，将去马赛克问题转化为压缩感知的信号重构问题；最后，采用改进的光滑0范数和修正牛顿法的重构算法求解去马赛克问题，得到重构的多光谱图像。仿真实验表明，相对于基于克罗内克压缩感知和组稀疏两种算法，本文算法提高了重构的多光谱图像的峰值信噪比，能有效减少对比算法重构多光谱图像中出现的锯齿现象，改善了重构图像具有更好的视觉效果。实验结果验证了本文算法的有效性。

In order to overcome shortcomings such as the low efficiency and the large calculation of multi-spectral image demosaicking algorithm on MSFA pattern,a new method of spectral image dem-osaicking algorithm is proposed.First,the equivalence between the problem of demosaicking and the compressed sensing is analyzed.Then a model of the multi-spectral image demosaicking algorithm is given by considering compressed sensing.The discrete cosine transform is used to construct the sparse base of the compressed sensing.The problem of multi-spectral demosaicking of MSFA pattern is transformed into the problem of sparse signal reconstruction in compressed sensing.Finally,the New-ton Smooth L0 Norm algorithm is used to reconstruct the multi-spectral image.The experimental re-sults show that the proposed method can effectively reduce the aliasing appears on the present demo-saicking algorithm.The results show that the peak signal to noise ratio of the algorithm in this paper is compared with that of based on Kronecker,and the group sparse of two algorithm is significantly improved.The experimental results verify the effectiveness of the proposed algorithm.