The Imaging Science Subsystem (ISS) mounted on Cassini spacecraft took images of Saturn's inner satellites between 2004 and 2017. In some of these images, the satellites are so close to Saturn rings that their images are affected by the scattered light from Saturn rings, which results in poor, even impossible, measurements of targets. A background removal algorithm is proposed to measure such images. A total of 70 ISS images of seven inner satellites near Saturn rings (Janus, Epimetheus, Atlas, Prometheus, Pandora, Methone, Anthe) have been reduced by using the proposed method. Compared with the results from the method without removing the background affected by scattered light, the proposed method demonstrates an improvement in accuracy of at least 43%. The final results show that the residuals of these measurements relative to the JPL ephemeris SAT415 have means of about 0.72 km and 2.26 km in right ascension (α) and declination (delta), with standard deviations of 10.99 km and 11.36 km, respectively.