We propose accelerated implementations of bilateral filter (BF) and nonlocal means (NLM) called color-compressive bilateral filter (CCBF) and color-compressive nonlocal means (CCNLM). CCBF and CCNLM are random filters, whose Monte-Carlo averaged output images are identical to the output images of conventional BF and NLM, respectively. However, CCBF and CCNLM are considerably faster because the spatial processing of multiple color channels are combined into a single random filtering process. This implies that the complexity of CCBF and CCNLM is less sensitive to color dimension (e.g., hyperspectral images) relatively to other BF and NLM methods. We experimentally verified that the execution time of CCBF and CCNLM are faster than the existing “fast” implementations of BF and NLM, respectively.