We establish a practical regularized least-squares model with adaptive regularization for dealing with blur and mixed noise in images. This model has some advantages, such as good adaptability for edge restoration and noise suppression due to the application of a priori spatial information obtained from a polluted image. We further focus on finding an important feature of image restoration using an adaptive restoration model with different regularization parameters in polluted images. A more important observation is that the gradient of an image varies regularly from one regularization parameter to another under certain conditions. Then, a modified graduated nonconvexity approach combined with a median filter version of a spatial information indicator is proposed to seek the solution of our adaptive image-restoration model by applying variable splitting and weighted penalty techniques. Numerical experiments show that the method is robust and effective for dealing with various blur and mixed noise levels in images.