The gridding method for image reconstruction by Fourier transformation

Area of Science:

• Computational imaging
• Signal processing

Background:

• Reconstructing signals from Fourier transform data is crucial in many scientific fields.
• Traditional interpolation methods can be error-prone due to noise and sampling limitations.

Purpose of the Study:

• To introduce a novel computational method for reconstructing n-dimensional signals from their sampled Fourier transforms.
• To provide a more accurate and efficient alternative to existing reconstruction techniques.

Main Methods:

• The method involves convolving the signal's Fourier transform with a window function on a Cartesian grid.
• Numerical computation of the convolution is followed by an inverse discrete Fourier transform.
• The final signal is obtained by dividing the result by the window function.

Main Results:

• The convolution's smoothing effect reduces errors compared to simple interpolation.
• The method is applicable to diverse reconstructive imaging modalities like radio astronomy, MRI, and CT.
• It offers a fast and accurate alternative to filtered backprojection.

Conclusions:

• The proposed computational method provides a robust approach for signal reconstruction from sampled Fourier transforms.
• Its versatility extends to various imaging applications and offers advantages over traditional methods.
• Variants of the method have further applications in signal resampling and transform computation.