To address the problem that existing terahertz imaging systems require complex and expensive hardware equipment, a continuous-wave terahertz imaging system based on single-image super-resolution reconstruction is designed to reduce equipment complexity and hardware cost. By preprocessing the terahertz images generated by this imaging system in two dimensions, the occupied memory of image processing is reduced and the speed of subsequent processing is increased. A restricted-contrast adaptive histogram equalization algorithm is introduced for sub-regional contrast enhancement of terahertz images to effectively solve the problem of low contrast of terahertz images. The super-resolution reconstruction of terahertz images is achieved by using sparse representation and dictionary learning, and the algorithm of inverse cosecant fitted with Newtonian smoothing zero parity is proposed to solve the zero-norm optimization problem and improve the reconstruction accuracy. By performing super-resolution reconstruction of single terahertz images acquired by this imaging system, the algorithm improves 3.232 in edge intensity and 0.300 in mean gradient comparison, which verifies the effectiveness and superiority of super-resolution reconstruction of single terahertz images.