Semi-Tensor Compressed Sensing for Hyperspectral Image

Compressed sensing (CS) technique contributes to reduce the burden of storage and transmission for hyperspectral images (HSIs) which are large 3D data cubes. Previous CS methods usually adopt sensing matrixes whose column number is equal to the length of the signal to sample data. As the length of the signal increases, the sensing matrix can be very large, especially for high-dimensional hyperspectral data. To overcome the drawback, a new semi-tensor based CS (ST-CS) method is proposed to for HSIs. In the sampling model, we construct a semi-tensor sensing matrix whose column number is much smaller than the length of spectral pixel. Then, the semi-tensor product, which breaks the dimension matching condition for matrix multiplication, is applied to the data sampling. The lower-dimensional sensing matrixes can reduce the data storage in the onboard system. In the sparse coding and reconstruction model, the spatial correlation of spectral pixels is exploited by introducing a regularization. The regularization tries to push reconstructed neighboring pixels to be similar. As a consequence, some unsuccessfully reconstructed pixels may be corrected by the use of neighbor information. Furthermore, the spatial structure of the HSI can be better reconstructed. Experimental results show the effectiveness of the proposed method.