The scattering phenomena prevents traditional optical systems from directly observing the target object behind a random medium, allowing only the collection of speckle images. The quality of a target recovered from speckle images is limited not only by algorithm parameters, but also by scattering distance and the employed optical imaging system. To improve the quality of speckle image restoration, this paper relates the image restoration quality to focal length and object length and proposes an optimal imaging-parameter model. Clear speckle images are collected after changing the lens focal length and adjusting the target spectrum information obtained by the camera. Applying the speckle correlation principle and a phase restoration algorithm, objects passing through a scattering medium are restored in the speckle image. The simulation and experimental results show that when the scattering distance is 0.5 m and the focal length is increased from 18 mm to 55 mm, the effective aperture of the lens enlarges and more complete spectral information of the object is preserved. The similarity of the target object structure increases from 0.3824 to 0.7829, enhancing the recovery effect. Adjusting the algorithm parameters optimizes the quality of speckle reconstruction at short focal lengths. At a focal length of 45 mm, the structural similarity increases from 0.6341 to 0.7626 but the restoration effect is non-ideal. After increasing the scattering distance, the image reconstruction effect decreases and the scattering medium can be imaged using longer focal length lenses.