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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

Summary

This summary is machine-generated.

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.

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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.

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.