为了提高模糊加噪声图像的恢复质量，提出了一种用于图像恢复处理的改进的带约束的正则化模型。该模型首先利用Levine等人提出的变指数、线性增长函数作为正则项，并根据图像局部特征选择合适的正则参数，这样既保留了总变差正则化方法在恢复图像边缘方面的优势，又减少了梯子现象；其次，为进一步提高恢复图像的质量，在此基础上再添加有界约束条件，如将灰度值固定在某范围内，以形成约束优化问题。由于它的求解相对复杂，为此可应用原对偶积极集法求解，其实质就是用半光滑Newton法来求解由约束优化问题转化所得到的方程组。数值实验表明，此方法是可行的和有效的。

In this paper, a modified bound constrained regularization model was proposed for image denoising and deblurring. In the model, we choose the variable exponent linear growth function proposed by Levine as the regularization term and choose the regularization parameters adaptively according to the image local feature. It not only preserves the advantage of the total variation regularization model, but also reduces staircase. Then, we introduce some bound constraints to the modified model, such as limit the range of u, to improve the quality of the restored image. At last, the constrained minimization problems are solved by primal-dual active-set method, essentially a semi-smooth Newton’s method. The numerical results show that our method is feasible and valid.