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 analytical 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.