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Phase selection of synthetic discriminant function filters.

P Refregier, J P Huignard

|June 26, 2010

Summary

Selecting correlation peak phases for synthetic discriminant function filters involves trade-offs. Optimizing correlation peak sharpness is often more beneficial than solely minimizing output variance for these filters.

Area of Science:

Optics and photonics
Signal processing
Machine learning

Background:

Synthetic discriminant function (SDF) filters are widely used in pattern recognition.
Phase selection in SDF filters significantly impacts performance.
Minimizing output variance and optimizing correlation peak shape are key considerations.

Purpose of the Study:

To analyze the complexity of correlation peak phase selection for SDF filters.
To compare the benefits of minimizing output variance versus optimizing correlation peak form.
To propose a general framework for phase selection in SDF filters.

Main Methods:

Mathematical analysis of correlation peak phase selection.
Comparison of output variance minimization and correlation peak form optimization.

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Illustrative examples using the proposed framework.

Main Results:

Minimizing output variance and optimizing correlation peak form are of equivalent complexity.
Variance reduction through phase selection can be advantageous in specific scenarios.
Optimizing correlation peak sharpness often yields more significant performance improvements.

Conclusions:

The choice of phase selection strategy for SDF filters depends on the application.
Optimizing correlation peak sharpness is frequently a more fruitful approach than solely minimizing variance.
The proposed framework aids in understanding and selecting optimal phase selection strategies.