Speckle noise is problematic in optical coherence tomography (OCT) and often obscures the structure details. In this paper, we propose a new method to reduce speckle noise from multiply scanned OCT slices. The proposed method registers the OCT scans using a global alignment followed by a local alignment based on global and local motion estimation. Then low rank matrix completion using bilateral random projection is utilized to estimate the noise and recover the clean image. Experimental results show that the proposed method archives average contrast to noise ratio 14.90, better than 13.78 by the state-of-the-art method used in current OCT machines. The technology can be embedded into current OCT machines to enhance the image quality.