A constrained optimization approach to combining multiple non-local means denoising estimates

•We solve an optimization problem to combine multiple estimates of a denoised image.•A sum of risk and gradient penalties is minimized, and positivity is required.•We combine multiple NLM estimates created with different parameter choices.•Experimental results show improvement re other NLM methods.•By combining several estimates, sensitivity to parameter selection is reduced.

There is an ongoing need to develop image denoising approaches that suppress noise while maintaining edge information. The non-local means (NLM) algorithm, a widely used patch-based method, is a highly effective edge-preserving technique but is sensitive to parameter tuning. We use a variational approach to combine multiple NLM estimates, seeking a solution that balances positivity constraints and gradient penalties against Stein's Unbiased Risk Estimate (SURE). This method greatly reduces parameter sensitivity and improves denoising performance vs. other NLM variants.