This paper proposes an adaptive sparse domain selection (ASDS) and adaptive regularization (AReg) approach for image deblurring and super-resolution. The method leverages sparse representation and adaptive regularization to enhance image restoration performance. The key contributions include: (1) learning multiple compact sub-dictionaries from example image patches to adaptively select the most suitable sparse domain for each local image patch; (2) introducing two adaptive regularization terms: autoregressive (AR) models to regularize local image structures and non-local self-similarity to preserve edges and suppress noise; and (3) adaptively estimating the sparsity regularization parameter for improved performance. The proposed method is validated on image deblurring and super-resolution tasks, achieving superior results in terms of PSNR and visual perception compared to state-of-the-art algorithms. The ASDS-AReg framework combines adaptive sparse domain selection with adaptive regularization to effectively reconstruct image details. The algorithm is implemented using an efficient iterative shrinkage approach to solve the $ l_1 $-minimization problem. The method is tested on various image restoration tasks, demonstrating its effectiveness in handling different types of image degradation. The results show that the proposed approach outperforms existing methods in both quantitative and qualitative aspects.This paper proposes an adaptive sparse domain selection (ASDS) and adaptive regularization (AReg) approach for image deblurring and super-resolution. The method leverages sparse representation and adaptive regularization to enhance image restoration performance. The key contributions include: (1) learning multiple compact sub-dictionaries from example image patches to adaptively select the most suitable sparse domain for each local image patch; (2) introducing two adaptive regularization terms: autoregressive (AR) models to regularize local image structures and non-local self-similarity to preserve edges and suppress noise; and (3) adaptively estimating the sparsity regularization parameter for improved performance. The proposed method is validated on image deblurring and super-resolution tasks, achieving superior results in terms of PSNR and visual perception compared to state-of-the-art algorithms. The ASDS-AReg framework combines adaptive sparse domain selection with adaptive regularization to effectively reconstruct image details. The algorithm is implemented using an efficient iterative shrinkage approach to solve the $ l_1 $-minimization problem. The method is tested on various image restoration tasks, demonstrating its effectiveness in handling different types of image degradation. The results show that the proposed approach outperforms existing methods in both quantitative and qualitative aspects.