Direct Fourier Tomographic Reconstruction Image-To-Image Filter

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We present an open-source ITK implementation of a direct Fourier method for tomographic reconstruction, applicable to parallel-beam x-ray images. Direct Fourier reconstruction makes use of the central-slice theorem to build a polar 2D Fourier space from the 1D transformed projections of the scanned object, that is resampled into a Cartesian grid. Inverse 2D Fourier transform eventually yields the reconstructed image. Additionally, we provide a complex wrapper to the BSplineInterpolateImageFunction to overcome ITK’s current lack for image interpolators dealing with complex data types. A sample application is presented and extensively illustrated on the Shepp-Logan head phantom. We show that appropriate input zeropadding and 2D-DFT oversampling rates together with radial cubic b-spline interpolation improve 2D-DFT interpolation quality and are efficient remedies to reduce reconstruction artifacts.
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plus Automatic Testing Results by Insight-Journal Dashboard on Fri Aug 24 06:33:51 2007 for revision #1
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minus Direct Fourier Reconstruction by Wesley Turner on 2009-04-23 13:24:36 for revision #2
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The authors provide an image to image filter sufficient to do discrete fourier reconstruction of sinogram to image data.  The filter has parameters to adjust the reconstruction to allow for image padding, resampling, and interpolation order.  In addition, the authors provide a Bspline interpolation class for complex data.


The hypothesis is that they can support direct FFT tomographic reconstruction in the ITK environment for parallel beam CT sinogram data.


The authors provide a code implementation and a test input/output image pair that provide evidence the filter works as described.

Open Science:

Source code for the reconstruction algorithm, the bspline interpolator, and test drivers are provided; as are input and output images.


I downloaded, compiled and ran the code.  The code passed their test and manual comparison of the target output image to that generated by the provided code gives qualitatively identical results.  The provided paper provides a good overview of the algorithm and sufficient detail so as to understand the provided code.

There was one small compilation error under VS9 where the compiler was unable to properly determine which atan function (float atan(float) or double atan(double)) at line 27 of itkDirectFourierReconstructionImageToImageFilter.txx.  By making the provided argument a double, this compilation error was removed.

Quality of the data :

Data is derived from a standard phantom and is easy to use.

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Categories: Blurring filters, Derivatives and Integrals, Filtering, Geometric transforms, Mathematics, Resampling
Keywords: Tomographic Reconstruction, CT, Direct Fourier Method, Image-To-Image Filter
Toolkits: ITK, CMake
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