The image super-resolution (SR) reconstruction technology based on the micro-scanning system is one of the best methods for realizing high-resolution infrared imaging. Thus, in this work, we first present a frequency domain phase-based projection onto convex sets SR reconstruction algorithm. This method takes advantage of the texture details and contrast-independent feature of the phase information in the frequency domain and can be used to realize image denoising and SR reconstruction for the infrared image simultaneously. We also propose the use of an image quality assessment metric based on the frequency domain phase spectrum. Second, we design and realize an infrared micro-scanning optical system to obtain sub-pixel low-resolution images for SR reconstruction. The infrared micro-scanning optical system we constructed can realize controllable sub-pixel micro-scanning of an arbitrary step size. Furthermore, we can realize sub-pixel low-resolution image collection by moving two light and compact pieces instead of moving the entire lens, sensor array, or sample-as in the traditional method. Thus, the precision of the sub-pixel movements can be greatly improved. Using our proposed algorithm and infrared micro-scanning optical system, we realize infrared SR imaging in both simulations and experiments.