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.