Insufficient spatial resolution of detectors is an obstacle to capturing spectra with high resolution. An effective solution is sub-pixel restoration, which can restore a high resolution spectrogram from sub-pixel shifted low resolution ones. In the present paper, an algorithm for sub-pixel restoration is suggested. It utilizes the bidirectional recursive relation between sub-pixel values and estimates each sub-pixel value from both directions of head-end and end-head. As a result, the averaged value will be accepted as the sub-pixel value. Numerical experiments on single gauss profile and superposition ones verified the effectiveness of the algorithm.