联合低秩与稀疏先验的高光谱图像压缩感知重建

摘要

A new compressed sensing model is proposed to reconstruct hyperspectral image .In the encoder side ,block-dialog measurement matrix formed by permuted noiselets transform is used to randomly measure the signal of each channel independently . In the decoder side ,the low rank and sparse representation models are firstly constructed to decompose hyperspectral data matrix into low rank and sparse parts ,and the low rank part is further sparsely decomposed .Then ,the intra-channel low rank prior and the inter-channel sparse prior are jointly utilized to reconstruct the compressed data .A numerical optimization algorithm is also proposed to solve the reconstruction model by augmented lagrange multiplier method .Every sub-problem in the iteration formula admits analyti-cal solution after introducing auxiliary variable and linearization operation .The complexity of the numerical optimization algorithm is reduced .The experimental results verify the effectiveness of our algorithm .%本文建立了一种新的高光谱图像压缩感知重建模型，编码端采用块对角的Noiselet测量矩阵对每一谱带进行独立采样，解码端首先建立高光谱图像低秩稀疏表示模型，分解为低秩与稀疏成分，并对低秩成分在空间维进行稀疏分解，进而构建联合谱间低秩性先验与谱内空间稀疏性先验的凸优化重建模型，并提出模型求解的增广拉格朗日乘子迭代算法，通过引入辅助变量与线性化技巧，使得每一子问题均存在解析解，降低了模型求解的复杂度。实验结果验证了本文模型及其算法的有效性。