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Non-Local Means (NLM) and its variants have proven to be effective and robust in many image denoising tasks. In this letter, we study approaches to selecting center pixel weights (CPW) in NLM. Our key contributions are 1) we give a novel formulation of the CPW problem from a statistical shrinkage perspective; 2) we construct the James-Stein shrinkage estimator in the CPW context; and 3) we propose a new local James-Stein type CPW (LJSCPW) that is locally tuned for each image pixel. Our experimental results showed that compared to existing CPW solutions, the LJSCPW is more robust and effective under various noise levels. In particular, the NLM with the LJSCPW attains higher means with smaller variances in terms of the peak signal and noise ratio (PSNR) and structural similarity (SSIM), implying it improves the NLM denoising performance and makes the denoising less sensitive to parameter changes.