Hashed nonlocal means for rapid image filtering

Denoising algorithms can alleviate the trade-off between noise-level and acquisition time that still exists for certain image types. Nonlocal means, a recently proposed technique, outperforms other methods in removing noise while retaining image structure, albeit at prohibitive computational cost. Modifications have been proposed to reduce the cost, but the method is still too slow for practical filtering of 3D images. This paper proposes a hashed approach to explicitly represent two summed frequency (hash) functions of local descriptors (patches), utilizing all available image data. Unlike other approaches, the hash spaces are discretized on a regular grid, so primarily linear operations are used. The large memory requirements are overcome by recursing the hash spaces. Additional speed gains are obtained by using a marginal linear interpolation method. Careful choice of the patch features results in high computational efficiency, at similar accuracies. The proposed approach can filter a 3D image in less than a minute versus 15 minutes to 3 hours for existing nonlocal means methods.