Optical coherence elastography allows the characterization of the mechanical properties of tissues, and can be performed through estimating local displacement maps from subsequent acquisitions of a sample under different loads. This displacement estimation is limited by noise in the images, which can be high in dynamic systems due to the inability to perform long exposures or B-scan averaging. In this work, we propose a framework for simultaneously enhancing both the image quality and displacement map for elastography, by motion compensated denoising with the block-matching and 4D filtering (BM4D) method, followed by a re-estimation of displacement. We adopt the interferometric synthetic aperture microscopy (ISAM) method to enhance the lateral resolution away from the focal plane, and use sub-pixel cross correlation block matching for non-uniform deformation estimation. We validate this approach on data from a commercial spectral domain optical coherence tomography system, whereby we observe an enhancement of both image and displacement accuracy of up to 33% over a standard approach.