Speckle noise significantly limits the information content extraction provided by optical coherence tomography (OCT). Therefore speckle reduction is an important issue in OCT imaging. Using a method of regularization by minimizing Csiszar’s I-divergence, we derive a method of speckle minimization. This method can not only produce an image data that is consistent with the known data but also extrapolate additional detail. This algorithm is used to process the OCT image of the human finger. The results show that this method of speckle minimization can significantly reduce speckle and increase the signal-to-noise ratio, while preserve edge sharpness.