Non-local means image denoising with a soft threshold

Non-local means (NLM) are typically biased by the accumulation of small weights associated with dissimilar patches, especially at image edges. Hence, we propose to null the small weights with a soft threshold to reduce this accumulation. We call this method the NLM filter with a soft threshold (NLM-ST). Its Stein's unbiased risk estimate (SURE) approaches the true mean square error; thus, we can linearly aggregate multiple NLM-STs of Monte-Carlo-generated parameters by minimizing SURE to surpass the performance limit of single NLM-ST, which is referred to as the Monte-Carlo-based linear aggregation (MCLA). Finally, we employ a simple moving average filter to smooth the MCLA image sequence to further improve the denoising performance and stability. Experiments indicate that the NLM-ST outperforms the classic patchwise NLM and three other well-known recent variants in terms of the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and visual quality. Furthermore, its PSNR is higher than that of BM3D for certain images.