An MMSE approach to nonlocal image denoising: Theory and practical implementation

Chul Lee, Chulwoo Lee, Chang-Su Kim

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


A nonlocal minimum mean square error (MMSE) image denoising algorithm is proposed in this work. Based on the Bayesian estimation theory, we first derive that the conventional nonlocal means filter is an MMSE estimator in the special case of noise-free nonlocal neighbors. Then, we develop the nonlocal MMSE denoising filter that can minimize the mean square error (MSE) of a denoised block in more general cases of noisy nonlocal neighbors. Furthermore, the proposed algorithm searches nonlocal neighbors from an external database as well as the entire input image to improve the performance even when a noisy block may not have similar blocks within the image. Since the extended search range demands a higher computational burden, we develop a probabilistic tree-based search method to reduce the computational complexity. Simulation results show that the proposed algorithm provides significantly better denoising performance than the conventional nonlocal means filter.

Original languageEnglish
Pages (from-to)476-490
Number of pages15
JournalJournal of Visual Communication and Image Representation
Issue number3
Publication statusPublished - 2012 Apr

Bibliographical note

Funding Information:
This work was supported partly by the Global Frontier R&D Program on Human-centered Interaction for Coexistence, funded by the NRF of Korea grant funded by the Korean Government (MEST) (NRF-M1AXA003-2011-0031648), and partly by Basic Science Research Program through the NRF funded by the MEST (2011- 0001271).


  • Bayesian estimation
  • External database
  • Image denoising
  • Image restoration
  • Minimum mean square error (MMSE) denoising
  • Noisy nonlocal neighbors
  • Nonlocal means filter
  • Probabilistic tree search

ASJC Scopus subject areas

  • Signal Processing
  • Media Technology
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


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