In ultrasound elastography, tissue axial strains are obtained through the differentiation of axial displacements. However, the application of the gradient operator amplifies the noise present in the displacement rendering unreadable axial strains. In this paper a novel denoising scheme based on repeated filtering in consecutive fractional Fourier transform domains is proposed for the accurate estimation of axial strains. The presented method generates a time-varying cutoff threshold that can accommodate the discrete non-stationarities present in the displacement signal. This is achieved by means of a filter circuit which is composed of a small number of ordinary linear low-pass filters and appropriate fractional Fourier transforms. We show that the proposed method can improve the contrast-to-noise ratio (CNR(e)) of the elastogram outperforming conventional low-pass filters.