AbstractSuper‐resolution image reconstruction refers to obtaining an image at a resolution higher than that of a camera (sensor) used in recording the image. In this paper, we present a new joint minimization model in which an objective function is set up consisting of three terms: the data fitting term, the regularization terms for the reconstructed image and the observed low‐resolution images. An alternating minimization iterative algorithm is proposed and developed to reconstruct the image. We give a convergence analysis of the alternating minimization iterative algorithm and show that it converges forH1‐norm regularization functional. Numerical examples are given to illustrate the effectiveness of the joint minimization model and the efficiency of the algorithm. Copyright © 2004 John Wiley & Sons, Ltd.