Second (and final) part of the implementation of the Direct Fourier Reconstruction with Fourier − instead of Hartley − Transform...
1- Script: Computing 2D reconstruction image
As summarized in Fig. 1, the script takes as input the stack of 1D FTs − calculated previously from the sinogram [Link] − and then fills the 2D Fourier Space depending of interpolation scheme − Nearest or Bilinear whose implementation is described in this post [Link]− .
For sake of convenience, two additional methods getComplex(...) and setComplex(...) are added to read/write the real and imaginary parts in the 2D Fourier stack.
The output image is the 2D Fourier stack.
+++ JavaScript IJ snippet: FourierRec_FFT.js +++
+++ End of JavaScript IJ snippet +++
2- Results
To get the final image, click on the stack entitled "Complex of RecDirect" and process an inverse FFT (Process > FFT > Inverse FFT), to get the image of Fig. 2. Finally, swap the quadrants (Process > FFT > Swap Quadrants).Fig.2: Image obtained after computing an Inverse Fourier Transform of the image created by the script FourierRec_FFT.j. In this case, the sinogram was previously zero-padded. |
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