Edge-preserving image regularization based on Morphological Wavelets and Dyadic Trees

Zhen James Xiang, Peter Jeffrey Ramadge

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Despite the tremendous success of wavelet-based image regularization, we still lack a comprehensive understanding of the exact factor that controls edge preservation and a principled method to determine the wavelet decomposition structure for dimensions greater than 1. We address these issues from a machine learning perspective by using tree classifiers to underpin a new image regularizer that measures the complexity of an image based on the complexity of the dyadic-tree representations of its sublevel sets. By penalizing unbalanced dyadic trees less, the regularizer preserves sharp edges. The main contribution of this paper is the connection of concepts from structured dyadic-tree complexity measures, wavelet shrinkage, morphological wavelets, and smoothness regularization in Besov space into a single coherent image regularization framework. Using the new regularizer, we also provide a theoretical basis for the data-driven selection of an optimal dyadic wavelet decomposition structure. As a specific application example, we give a practical regularized image denoising algorithm that uses this regularizer and the optimal dyadic wavelet decomposition structure.

Original languageEnglish (US)
Article number6111480
Pages (from-to)1548-1560
Number of pages13
JournalIEEE Transactions on Image Processing
Issue number4
StatePublished - Apr 2012

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design


  • Image enhancement
  • morphological operations
  • multidimensional signal processing
  • wavelet transforms


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