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.