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Nonlinear multiresolution signal decomposition schemes--part I: morphological pyramids.

J Goutsias1, H M Heijmans

  • 1Dept. of Electr. and Comput. Eng., Johns Hopkins Univ., Baltimore, MD 21218, USA. goutsias@jhu.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 12, 2008
PubMed
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This study introduces a general theory for creating linear and nonlinear pyramid decomposition schemes for signal processing. This framework unifies various methods, enabling advanced signal analysis and synthesis.

Area of Science:

  • Signal Processing
  • Image Analysis
  • Multiresolution Techniques

Background:

  • Multiresolution techniques, particularly pyramid decomposition, are gaining importance in signal processing.
  • Existing pyramid decomposition schemes vary in their approaches to signal analysis and synthesis.

Purpose of the Study:

  • To present a general theory for constructing both linear and nonlinear pyramid decomposition schemes.
  • To establish a unified framework for diverse pyramid-based signal analysis and synthesis methods.

Main Methods:

  • The proposed theory utilizes a multi-level structure where information content decreases at higher levels.
  • Analysis operators reduce information for higher levels, while synthesis operators preserve information for lower levels.
  • A key assumption is that synthesis followed by analysis results in the identity operator, ensuring no information loss.

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Main Results:

  • The theory encompasses various existing schemes, including linear pyramids, morphological skeleton decompositions, morphological Haar pyramids, and median pyramids.
  • A distinction is made between single-scale and multiscale decomposition schemes based on sample reduction.
  • The theory provides a foundation for developing nonlinear wavelet decomposition schemes and filter banks.

Conclusions:

  • The presented general theory offers a unified approach to pyramid decomposition for signal processing.
  • This framework facilitates the construction of novel linear and nonlinear signal analysis and synthesis methods.
  • The work lays the groundwork for advancements in nonlinear wavelet decomposition and filter bank design.