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Local cosine bases in two dimensions.

¹Innovations for Lucent Technol., Bell Lab., Murray Hill, NJ.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 1, 1997

Summary

This study introduces two-dimensional local cosine bases for discrete time signals on both rectangular and nonrectangular lattices. Nonrectangular cases are simplified by transforming them into one-dimensional problems.

Area of Science:

Signal Processing
Applied Mathematics
Numerical Analysis

Background:

Local cosine bases are essential for time-frequency analysis.
Discrete signal processing requires efficient basis construction methods.
Handling nonrectangular data structures poses unique challenges.

Purpose of the Study:

To construct two-dimensional (2-D) local cosine bases in discrete time.
To provide solutions for both rectangular and nonrectangular lattices.
To simplify the analysis of nonrectangular data.

Main Methods:

Development of 2-D local cosine basis construction algorithms.
Application of mapping techniques to convert 2-D nonrectangular problems into 1-D equivalents.
Discrete time signal processing methodologies.

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Main Results:

Successful construction of 2-D local cosine bases for discrete time signals.
Demonstrated applicability to rectangular lattices.
Effective transformation and solution for nonrectangular lattices via 1-D mapping.

Conclusions:

The proposed method provides a unified approach for constructing 2-D local cosine bases.
The mapping technique offers an efficient way to handle complex nonrectangular lattice structures.
This work advances discrete signal processing techniques for diverse lattice types.