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A Hankel transform approach to tomographic image reconstruction.

W E Higgins¹, D R Munson

¹Biodynamics Res. Unit, Mayo Clinic, Rochester, MN.

IEEE Transactions on Medical Imaging

|January 1, 1988

Summary

A new Hankel-transform-reconstruction (HTR) algorithm reconstructs 2D images from projections. This polar-coordinate based method shows performance comparable to existing convolution-backprojection techniques.

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Area of Science:

Image reconstruction
Computational imaging
Signal processing

Background:

Image reconstruction from projections is crucial in various scientific fields.
Existing algorithms like convolution-backprojection have limitations.
Novel algorithms are needed for improved accuracy and efficiency.

Purpose of the Study:

To introduce and evaluate a novel algorithm for 2D image reconstruction.
To present the Hankel-transform-reconstruction (HTR) algorithm.
To compare HTR algorithm performance against established methods.

Main Methods:

Developed a polar-coordinate based algorithm (HTR).
Expanded the polar-form Fourier transform into a Fourier series.
Calculated Hankel transforms of series coefficients.
Reconstructed the image in polar coordinates and interpolated to a rectilinear grid.

Main Results:

The HTR algorithm successfully reconstructs 2D images from sampled projections.
Performance of the HTR algorithm was found to be favorable.
Comparison showed comparable results to the convolution-backprojection algorithm.

Conclusions:

The Hankel-transform-reconstruction (HTR) algorithm is a viable new method for image reconstruction.
HTR offers a competitive alternative to existing reconstruction techniques.
Further exploration of the HTR algorithm is warranted.