To address the clarity degradation caused by scattering in underwater imaging, we propose a self-constructed Mach-Zehnder interference optical path to achieve image refocusing through a cloudy liquid using the transmission matrix method. We investigate the refocusing imaging effect using the intensity averaging method and Gerchberg-Saxton (GS) algorithm. Results indicate that the preset image can be clearly refocused through cloudy media using the four-step phase-shifting transmission matrix method. The cosine similarity ratio between the refocused and original images is determined to be 0.66 using intensity averaging, while this ratio is determined to be 0.91 using the GS algorithm. Combining the transmission matrix method with the GS algorithm effectively reduces the impact of scattering effects on image transmission. This approach has substantial application potential in oceanography, biomedical imaging, underwater communication, and other fields.