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Optical Scatter Microscopy Based on Two-Dimensional Gabor Filters

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Published on: June 2, 2010

An efficient algorithm to compute the complete set of discrete Gabor coefficients.

L Wang¹, C T Chen, W C Lin

¹Dept. of Electr. Eng. and Comput. Sci., Northwestern Univ., Evanston, IL.

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

|January 1, 1994

Summary

A new discrete Gabor transform algorithm efficiently calculates Gabor coefficients for discrete signals. This method allows exact signal reconstruction and utilizes Fast Fourier Transform (FFT) algorithms for computation.

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Area of Science:

Signal Processing
Applied Mathematics
Digital Signal Analysis

Background:

The Gabor transform, developed by Dennis Gabor in 1946, is a powerful tool for analyzing signals in both time and frequency domains.
Efficient computation of discrete Gabor coefficients and exact signal reconstruction have been areas of interest in digital signal processing.

Purpose of the Study:

To introduce an efficient algorithm for computing discrete Gabor coefficients of finite-duration discrete signals.
To enable exact reconstruction of the original signal from its discrete Gabor expansion coefficients.
To leverage existing Fast Fourier Transform (FFT) algorithms for computational efficiency.

Main Methods:

Development of a discrete Gabor transform algorithm based on finite summations.
Utilizing the mathematical similarities between the discrete Gabor transform and the discrete Fourier transform.
Demonstrating the applicability of Fast Fourier Transform (FFT) algorithms for computing discrete Gabor coefficients.

Main Results:

An efficient method for calculating the complete set of discrete Gabor coefficients for finite-duration discrete signals.
The capability to reconstruct the original signal exactly from the computed Gabor expansion coefficients.
The discrete 1-D Gabor transform algorithm is shown to be extendable to two-dimensional (2-D) applications.

Conclusions:

The presented discrete Gabor transform algorithm offers an efficient approach to signal analysis and reconstruction.
The algorithm's reliance on FFT principles ensures computational efficiency and broad applicability.
The extension to 2-D signals broadens the potential uses of this discrete Gabor transform method.