Aerothermal-induced intensity non-uniformity (NU) effects severely influence the effective performance of infrared (IR) imaging systems in high-speed flight. In this paper we propose a ℓp-regularized minimization method to remove intensity NU in IR images. Different from the existing NU correction methods, we consider and study important priors from the NU noise and the IR image, respectively. We assume spatial smoothness of the NU noise and piecewise continuity of the IR image, where the ℓp regularization term is employed in the correction model. A computationally efficient numerical algorithm based on half-quadratic regularization is adopted to solve the optimization problem. To tackle the non-convex ℓp-norm minimization sub-problem in this scheme, a generalized iterated shrinkage algorithm is used. Significant improvement on the image quality is obtained on both simulation and experimental studies. Both quantitative and qualitative comparisons to specialized state-of-the-art algorithms demonstrate its superiority.