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Updated: Jun 8, 2026
13:44
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
Summary
This study introduces Gabor
Area of Science:
- Signal Processing
- Mathematical Physics
Background:
- Gabor's signal expansion provides a method to decompose signals using shifted and modulated elementary signals.
- Understanding the relationship between Gabor expansion and spectral analysis is crucial for signal processing applications.
Purpose of the Study:
- To introduce Gabor's signal expansion and its connection to the sliding-window spectrum.
- To demonstrate the utility of the Zak transform in signal analysis and Gabor coefficient determination.
- To develop efficient computational methods for Gabor expansion coefficients.
Main Methods:
- Analysis of Gabor's expansion and its relation to the sliding-window spectrum.
- Introduction and application of the Zak transform for window function determination and coefficient calculation.
- Development of discrete Gabor and Zak transforms from continuous-time formulations.
Main Results:
- Gabor expansion coefficients are shown to be samples of the sliding-window spectrum.
- The Zak transform is demonstrated as a tool for finding appropriate window functions and expansion coefficients.
- Discrete transforms are introduced, enabling efficient computation analogous to the Fast Fourier Transform (FFT).
Conclusions:
- Gabor's expansion is intrinsically linked to spectral sampling.
- The Zak transform offers a powerful framework for analyzing Gabor expansions.
- Fast algorithms for discrete Gabor transform computation are established, enhancing practical signal analysis.
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