Image denoising based on nonlocal Bayesian singular value thresholding and Stein's unbiased risk estimator

Caoyuan Li, Hong Bo Xie*, Xuhui Fan, Yi Da Xu, Sabine Van Huffel, Scott A. Sisson, Kerrie Mengersen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


Singular value thresholding (SVT)- or nuclear norm minimization (NNM)-based nonlocal image denoising methods often rely on the precise estimation of the noise variance. However, most existing methods either assume that the noise variance is known or require an extra step to estimate it. Under the iterative regularization framework, the error in the noise variance estimate propagates and accumulates with each iteration, ultimately degrading the overall denoising performance. In addition, the essence of these methods is still least squares estimation, which can cause a very high mean-squared error (MSE) and is inadequate for handling missing data or outliers. In order to address these deficiencies, we present a hybrid denoising model based on variational Bayesian inference and Stein's unbiased risk estimator (SURE), which consists of two complementary steps. In the first step, the variational Bayesian SVT performs a low-rank approximation of the nonlocal image patch matrix to simultaneously remove the noise and estimate the noise variance. In the second step, we modify the conventional SURE full-rank SVT and its divergence formulas for rank-reduced eigen-triplets to remove the residual artifacts. The proposed hybrid BSSVT method achieves better performance in recovering the true image compared with state-of-the-art methods.

Original languageEnglish
Pages (from-to)4899-4911
Number of pages13
JournalIEEE Transactions on Image Processing
Issue number10
Publication statusPublished - Oct 2019

Scopus Subject Areas

  • Software
  • Computer Graphics and Computer-Aided Design

User-Defined Keywords

  • Image denoising
  • noise variance estimation
  • singular value thresholding
  • Stein's unbiased risk estimator
  • variational Bayesian inference


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