Accelerating non-local means algorithm with random projection

The non-local means (NLM) algorithm suppresses noise via replacing the noisy pixel by the weighted average of all the pixels with similar neighbourhood vectors. However, the weights calculation is computationally expensive, as a result of which the NLM algorithm is quite slow for practical applications. A random projection approach is introduced to reduce the dimension of neighbourhood vectors used in the NLM filtering process, which yields a faster and more accurate denoising effect. Experimental results illustrate the effectiveness of the proposed method.