Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency

Levent Şendur, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. In this paper, we will only consider the dependencies between the coefficients and their parents in detail. For this purpose, new non-Gaussian bivariate distributions are proposed, and corresponding nonlinear threshold functions (shrinkage functions) are derived from the models using Bayesian estimation theory. The new shrinkage functions do not assume the independence of wavelet coefficients. We will show three image denoising examples in order to show the performance of these new bivariate shrinkage rules. In the second example, a simple subband-dependent data-driven image denoising system is described and compared with effective data-driven techniques in the literature, namely VisuShrink, SureShrink, BayesShrink, and hidden Markov models. In the third example, the same idea is applied to the dual-tree complex wavelet coefficients.

Original languageEnglish (US)
Pages (from-to)2744-2756
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number11
StatePublished - Nov 2002


  • Bivariate shrinkage
  • Image denoising
  • Statistical modeling
  • Wavelet transforms

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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