We propose a fast and accurate solution to speckle reduction targeted specifically at optical coherence tomography images. The proposed speckle removing filter is designed using a novel potential function based on the gradient of the local variance of intensity. After filtering, the spatially neighboring pixels with close values of intensities converge to uniform gray values, while the edges remain intact. This filtering process results in removal of speckle without destroying the edges of the desired object. The proposed filter also prevents the generation of any false edges. Detailed experimental analysis shows at least 1-dB improvement in the peak signal-to-noise ratio for spectral domain optical coherence tomography images. The method also shows superior edge preservation, contrast, and speed compared to the state of the art in speckle removing filters. © 2013 IEEE.