An efficient computational scheme for the two-dimensional overcomplete wavelet transform

Ngai Fong Law, Wan Chi Siu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


We have studied the computational complexity associated with the overcomplete wavelet transform for the commonly used Spline wavelet family. By deriving general expressions for the computational complexity using the conventional filtering implementation, we show that the inverse transform is significantly more costly in computation than the forward transform. To reduce this computational complexity, we propose a new spatial implementation based on the exploitation of the correlation between the low-pass and the bandpass outputs that is inherent in the overcomplete representation. Both theoretical studies and experimental findings show that the proposed spatial implementation can greatly simplify the computations associated with the inverse transform. In particular, the complexity of the inverse transform using the proposed implementation can be reduced to slightly less than that of the forward transform using the conventional filtering implementation. We also demonstrate that the proposed scheme allows the use of an arbitrary boundary extension method while maintaining the ease of the inverse transform.
Original languageEnglish
Pages (from-to)2806-2819
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number11
Publication statusPublished - 1 Nov 2002


  • Computational complexity
  • Over-complete wavelets
  • Spatial implementation
  • Wavelet transform

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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