SURE-Based Non-Local Means

• Published in: IEEE signal processing letters Vol. 16; no. 11; pp. 973 - 976
• Main Authors: Van De Ville, D., Kocher, M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-11-2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Biomedical imaging; Biomedical measurements; Computational efficiency; Denoising; Exact solutions; Gaussian; Gaussian noise; Image restoration; Kernel; Mathematical analysis; Mean square error methods; Monitoring; Monitors; Noise reduction; non-local means; Optimization; Signal processing algorithms; Smoothing methods; Stein's unbiased risk estimate
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2009.2027669

Non-local means (NLM) provides a powerful framework for denoising. However, there are a few parameters of the algorithm-most notably, the width of the smoothing kernel-that are data-dependent and difficult to tune. Here, we propose to use Stein's unbiased risk estimate (SURE) to monitor the mean square error (MSE) of the NLM algorithm for restoration of an image corrupted by additive white Gaussian noise. The SURE principle allows to assess the MSE without knowledge of the noise-free signal. We derive an explicit analytical expression for SURE in the setting of NLM that can be incorporated in the implementation at low computational cost. Finally, we present experimental results that confirm the optimality of the proposed parameter selection.