In the commonly employed regularization models of image restoration and super-resolution (SR), the norm determination is often challenging. This paper proposes a method to adaptively determine the optimal norms for both fidelity term and regularization term in the (SR) restoration model. Inspired by a generalized likelihood ratio test, a piecewise function is proposed to solve the norm of the fidelity term. This function can find the stable norm value in a certain number of iterations, regardless of whether the noise type is Gaussian, impulse, or mixed. For the regularization norm, the main advantage of the proposed method is that it is locally adaptive. Specifically, it assigns different norms for different pixel locations, according to the local activity measured by a structure tensor metric. The proposed method was tested using different types of images. The experimental results and error analyses verify the efficacy of the method.