The accurate sparse coefficients were hard to be obtained from the degraded signal due to theimage noise. Aiming at this problem, a double l1 norm optimized image denoising algorithm via group sparse representation is studied. The algorithm constrains group sparse coefficients by using the l1 norm and sparse residual of sparse representation of non local similar image block as regularization item, and implements an optimal solution to the model for obtaining robust sparse coefficients by an effective iterative shrinkage algorithm. In addition, in order to further improve the performance of the image denoising algorithm, a Bayesian formula is used to derive a method for adaptively adjusting two regularization parameters. Extensive experimental results show that the proposed algorithm can suppress the artifacts while removing image noise, and preserve the detail of the image compared to many existing algorithms. Compared with the BM3D algorithm, our algorithm significantly improves the performance by 1.24 dB in PSNR.
