Optical coherence tomography (OCT) is a high-resolution noninvasive technology used in medical imaging for the spatial visualization of biological tissue. Due to its coherent nature, OCT suffers from speckle noise, which significantly degrades the information content of resulting scans. We introduce a new filtering method for three-dimensional OCT images, inspired by film grain removal techniques. By matching structural relatedness along all dimensions, the algorithm builds up vector paths for every voxel in the image volume representing its structural neighborhood. Then, by considering the information redundancy along these paths, our filter is able to reduce speckle noise significantly while simultaneously preserving structural information. This filter exceeds some common three-dimensional denoising algorithms used for OCT images, both in visual rendering quality and in measurable noise reduction. The noise-reduced results allow for improvement in subsequent processing steps, such as image segmentation.