Infrared (IR) sub-imaging guidance technique, which combines the single detector and optical scanning device, is a transition from point-source detection technique to imaging guidance technique. Infrared rosette scan sub-imaging system (IRSSIS) is a class of sub-imaging guidance system. The IRSSIS samples part data of the field of view (FOV) according to a specific pattern and obtains a sub-image including the position information of targets. Compressive imaging in the IRSSIS was studied inspired by the single pixel camera. Compressed sensing (CS) will help to reconstruct IR image in the condition of much fewer samples. The key problem of CS applied to the IRSSIS is the measurement matrix construction. While random measurement matrix has been studied intensively, it is hard to implement. A simple deterministic measurement matrix was proposed for the IRSSIS. Furthermore, a fast and effective recovery algorithm, optimized subspace pursuit algorithm (OSP), was proposed. Simulation results show that the proposed measurement matrices can compress and reconstruct IR image prior to the random Gaussian measurement matrices and random Bernoulli measurement matrices. The proposed recovery algorithm also has a better performance.