Abstract: According to the correlation analysis of Compressed Sensing (CS) measurements for hyperspectral images, a new reconstruction algorithm based on interband prediction and joint optimization is proposed. In the method, linear prediction is first applied to remove the correlations among successive hyperspectral measurement vectors. The obtained residual measurement vectors are then recovered using the proposed joint optimization based POCS (Projections Onto Convex Sets) algorithm with the steepest descent method. In addition, a pixel-guided stopping criterion is introduced to stop the iteration. Experimental results show that the proposed algorithm exhibits its superiority over other known CS reconstruction algorithms in the literature at the same measurement rates, while with a faster convergence speed.