Imaging through scattering media via speckle autocorrelation is a popular method based on the optical memory effect. However, it fails if the amount of valid information acquired is insufficient due to a limited sensor size. In this Letter, we reveal a relationship between the detector and object sizes for the minimum requirement to ensure image reconstruction by defining a sampling ratio R, and propose a method to enhance the image quality at a small R by capturing multiple frames of speckle patterns and piecing them together. This method will be helpful in expanding applications of speckle autocorrelation to remote sensing, underwater probing, and so on.