The repetitive interval is a very crucial feature of bands in print quality assessment, because any irregularity on the surface of a rotating component localized in the circumference will incur repetitive defects on the output of printer [1] [2] [3]. Hence, the repetitive interval can help us diagnose the issues. In previous work, a cost function method provides a robust algorithm to predict the repetitive interval on less noisy samples. However, if the samples contain more aperiodic bands and noise, the estimation will become a challenge. Moreover, the missing periodic bands will decrease the probability of correct prediction. In this paper, we proposes a novel cost-function-based repetitive interval estimation method for periodic bands. By adding synthetic missing bands, we re-evaluate the cost function values to check whether it has a better result. We also show the improvement of accuracy on the print samples with our proposed algorithm.<xref ref-type="corresp" rid="cor1">1</xref>