Super resolution methods alleviate the high cost and high difficulty in applying high resolution infrared image sensors. In this paper we present a novel single image super resolution method for infrared images by combining compressive sensing theory and deep learning. Low resolution images can be regarded as the compressed sampling results of the high resolution ones in compressive sensing. With sparsity in this theory, higher resolution images can be reconstructed. However, because of diverse level of sparsity for different images, the output contains noise and loss of high frequency information. Deep convolutional neural network provides a solution to relieve the noise and supplement some missing high frequency information. By concatenating two methods, we manage to produce better results in super resolution tasks for infrared images than SRCNN and ScSR. PSNR and SSIM values are used to quantify the performance. Applying our method to open datasets and actual infrared imaging experiments, we also find better visual results are preserved.