Abstract: Traditional regularized image de-blurring approach is easy to produce “artifact” effect like ringing and edge blur. In order to solve this problem, a sparsity regularized image deblurring model is proposed to restore the blurry image. The gross error function between estimation image and blurred image is used as data fidelity term and non-smooth regularization term is used for constraining the sparse representation coefficients over the sparse dictionary. A non-negative term is also added to ensure the positivity of the restored image. Furthermore, inspired from the alternating direction multiplier method, a multi-variable splitting fast iterative algorithm is proposed to solve the deblurring model numerically. The original problem is transformed into solving three simple sub-problems iteratively, thus computational complexity is decreased rapidly. Comprehensive experiments demonstrate that the proposed model and its numerical algorithm maintain the structure characteristics and smoothness of the image, and reduce the computational complexity.

Key words: sparse representation, variable splitting, alternating direction multiplier method, image deblurring

摘要： 传统的图像去模糊方法易产生振铃和边缘模糊等“伪像”效应，针对这一问题，采用非光滑的正则项约束图像在稀疏字典下表示系数的稀疏性，并引入非负约束项，提出了图像的稀疏正则化去模糊模型。进一步，基于交替方向拉格朗日乘子算法，提出了求解该模型的多变量分裂迭代快速算法，将复杂问题求解转化为三个简单子问题的迭代求解，降低了模型求解的复杂性。实验结果表明，所提出的去模糊模型及其快速算法相对较好地保持了图像的结构特征和平滑性，并降低了计算复杂性。

关键词: 稀疏表示, 变量分裂, 交替方向乘子, 去模糊