An approximately optimal subspace pursuit algorithm under cosparse analysis model was studied to reconstruct the original signal from the noisy measurement vectors.To overcome the drawbacks of the non steepest gradient during the pursuit process and the low successful reconstruction probability for sparse synthesis model

an approximately optimal subspace pursuit algorithm based on cosparse analysis model was presented and realized.The approximately optimal optimization object function for the algorithm was designed according to the structure of the different analysis dictionaries

the iterative pursuit process of the algorithm was revised

and the methods of selecting cosparsity was optimized.The simulation experiments show that the complete reconstruction probability of the new algorithm is evidently larger than that of the algorithm for ASP

AHTP

AIHT

AL1 and GAP when the cosparse operator is a random compact frame or a two dimension total variant matrix.The comprehensive average PSNR of the output signal for the new algorithm is larger than that of the algorithm of ASP

AHTP

and AIHT for 0.8dB

1.38dB and 3.13 dB respectively and is less than that of the algorithm of GAP and AL1 for 0.32 dB and 0.6dB when the input signal is with Gaussion noise.The complete reconstruction probability of the new algorithm was greatly improved by adopting the above measures

and the convergence condition for the new algorithm was simplified.