In the up-sampling process may occur effects like aliasing, blurring or noise addition which mainly affect the edges of the images. For those reasons is necessary to choose a method that preserves images quality so that these problems are minimized. In this paper, we present an alternative method to restore blurred images using linear programming to solve a minimization problem stated in the L1 norm. The model requires the blurred image and some prior knowledge about the blurring function type (Point spread function). In the proposed method we obtain a PSNR of 30 dB overcoming a classic bi-linear method by 4 dB in a set of thirty images from a cardiac MRI data set.