Speckle noise is problematic in optical coherence tomography (OCT). With the fast scan rate, swept source OCT scans the same position in the retina for multiple times rapidly and computes an average image from the multiple scans for speckle reduction. However, the eye movement poses some challenges. In this paper, we propose a new method for speckle reduction from multiply-scanned OCT slices. The proposed method applies a preliminary speckle reduction on the OCT slices and then registers them using a global alignment followed by a local alignment based on fast iterative diamond search. After that, low rank matrix completion using bilateral random projection is utilized to iteratively estimate the noise and recover the underlying clean image. Experimental results show that the proposed method achieves average contrast to noise ratio 15.65, better than 13.78 by the baseline method used currently in swept source OCT devices. The technology can be embedded into current OCT machines to enhance the image quality for subsequent analysis.