An optimal nonlinear extension of linear filters based on distributed arithmetic
1Electrical Engineering Department, The University of Texas at San Antonio, San Antonio, TX 78249, USA. dakopian@utsa.edu
Summary
This study introduces nonlinear filters for distributed arithmetic (DA) implementations, improving noise filtering without added complexity. Experiments show these nonlinear filters outperform optimal linear filters in real image processing tasks.
Area of Science:
- Digital Signal Processing
- Image Processing
- Computer Engineering
Background:
- Distributed arithmetic (DA) offers a multiplication-free approach for linear filters.
- Current DA implementations are limited to linear operations.
- Noise in images, especially non-Gaussian components, poses challenges for linear filters.
Purpose of the Study:
- To introduce a nonlinear extension of linear filters for DA-based implementations.
- To optimize the memory function (MF) under a mean-square error criterion.
- To enhance noise filtering capabilities, particularly for non-Gaussian and impulsive noise, without increasing computational complexity.
Main Methods:
- Developed a nonlinear extension of linear filters by optimizing the multivariate Boolean function (MF) memory function.
- Utilized a mean-square error criterion for optimization.
- Implemented and tested the proposed filters on real image datasets.
Main Results:
- The proposed nonlinear DA filters demonstrate superior performance compared to optimal linear filters in real image experiments.
- The nonlinear extension effectively filters noise, including non-Gaussian components.
- Variations of the filters were explored for impulsive noise removal and efficient processing of large data windows.
Conclusions:
- Nonlinear extensions of DA-based filters offer significant improvements over traditional linear filters.
- The proposed method provides an effective solution for noise reduction in image processing without compromising implementation complexity.
- Further research can explore optimized versions for specific noise types and processing requirements.
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