As subspace pursuit algorithm under cosparsity analysis model in compressed sensing has the shortcomings of low completely successful reconstruction probability and poor reconstruction performance, a cosparsity analysis subspace pursuit algorithm was proposed. The proposed algorithm was realized by adopting the selected random compact frame as the analysis dictionary and redesigning target optimization function. The selecting method of cosparsity value and the iterated process were improved. The simulation experiments show that the proposed algorithm has obviously higher completely successful reconstruction probability than that of Analysis Subspace Pursuit (ASP) and other five algorithms, and has higher comprehensive average Peak Signal-to-Noise Ratio (PSNR) for the reconstructed signal than that of ASP and other three algorithms, but a little bit lower than that of Gradient Analysis Pursuit (GAP) and other two algorithms when the original signal has Gaussion noise. The new algorithm can be used in audio and image signal processing.

To reconstruct the original signal from a set of linear measurements with noise, the cosparsity analytical model theory was analyzed and the hard thresholding orthogonal projection algorithm under the cosparsity analysis model was proposed. The cosparsity orthogonal projection strategy was used to improve the iterative process for the proposed algorithm, and the methods for selecting iterative step size and the length of cosparsity were given. The sufficient condition of convergence for the algorithm and the reconstructed signal error range between the reconstructed signal and the original one were provided. The experiments show that the CPU running time of the algorithm is only equal to 19%, 11% and 10% of AIHT, AL1 and GAP algorithms, and the average Peak Signal-to-Noise Ratio (PSNR) of reconstructed signal improves 0.89dB than that of AIHT but degrades a little bit than that of AL1 and GAP. It is concluded that the proposed algorithm can reconstruct the signal with Gaussion noise in high probability with very short running time or faster convergence speed than that of the current typical algorithm when some conditions are satisfied.