For the Gibbs artifact and "cracks" phenomenon which introduced by the Shearlet shrinkage denoising, a Shearlet adaptive shrinkage and nonlocal self-similarity model-based method for image denoising was proposed in this paper. First, the noisy image was firstly decomposed with multi-scale and multi-orientation by Shearlet transform. Second, based on the modeling of Shearlet coefficients by using Gaussian Scale Mixture (GSM) model, the image noises were reduced by adaptively approaching Shearlet coefficients with Bayesian least squares estimator, and then, the preliminary denoised image was reconstructed by inverse Shearlet transform. Finally, the preliminary denoised image was further filtered by nonlocal self-similarity model, and the final denoised image was produced. The experimental results show that the proposed method can better preserve the edge information. Meanwhile, it can effectively reduce the image noise and Gibbs-like artifacts produced by shrinkage. Compared with Non-Subsampled Shearlet Transform (NSST)-based image denoising with hard-thresholding, the proposed method improves the Peak-Signal to-Noise-Ratio (PSNR) and Structural Similarity (SSIM) by 1.41 dB and 0.08 respectively; compared with GSM model-based image denoising in the Shearlet domain, the proposed method improves the PSNR and SSIM by 1.04 dB and 0.045 respectively; compared with shearlet-based image denoising using trivariate prior model, the proposed method improves the PSNR and SSIM by 0.64 dB and 0.025 respectively.
