Many existing non-local means (NLM) methods either use Euclidean distance to measure the similarity between patches, or compute weight ωij only once and keep it unchanged during the subsequent denoising iterations, or use only the structure information of the denoised image to update weight ωij. These may lead to the limited denoising performance. To address these issues, this paper proposes the non-local adaptive means (NLAM) for image denoising. NLAM treats weight ωij as an optimization variable and iteratively updates its value. We then introduce three unbiased distances namely pixel-pixel, patch-patch, and coupled unbiased distances. These unbiased distances are more robust to measure the image pixel/patch similarity than Euclidean distance. Using the coupled unbiased distance, we propose the unbiased distance non-local adaptive means (UD-NLAM). Because UD-NLAM uses only a single patch size to compute weight ωij, we introduce multipatch UD-NLAM (MUD-NLAM) to adapt different noise levels. To further improve denoising performance, we then propose a new denoising method called MUD-NLAM with wavelet shrinkage (MUD-NLAM-WS). Experiment results show that the proposed NLAM, UD-NLAM and MUD-NLAM outperform existing NLM methods, and MUD-NLAM-WS achieves better performance than state-of-the-art denoising methods.