Part of the code has been borrowed from [5]. Thanks to R. Marabini for his lessons and insights on tomographic reconstruction techniques.

A CT scan or computed tomography scan (formerly known as computed axial tomography or CAT scan) is a medical imaging technique used in radiology to get detailed images of the body noninvasively for diagnostic purposes.

CT scanners use a rotating x-ray tube and a row of detectors placed in the gantry to measure X-ray attenuations by different tissues inside the body. The multiple X-ray measurements taken from different angles are then processed on a computer using reconstruction algorithms to produce tomographic (cross-sectional) images (virtual "slices") of a body [1].

Here, Filtered Back-projection algorithm is used to recontruct the 3D volume from the mentioned collection of X-ray measurements [3][4][5], or Sinograms, also known in mathematics as the Radon transform [2], an example of the 2D object Phantom and its Sinogram can be seen in Fig. 1.

Fig. 1. Radon transoform of Phantom image.

The data file './data/mouse.tif' contains a 3D sinogram that is used to reconstruct a 3D volume of the mouse, the steps followed are (1) extract 2D sinograms, (2) reconstruct each 2D sinogram, (3) stack the 2D reconstructions to form a reconstructed 3D folume, (4) generate a video of the 3D volume recontructed.

We use slice 201 as a reference to check our results with the ground truth ('./data/mouse_vol.tif'). We also use UCSF Chimera and ImageJ to explore the .tif files.

Fig. 2. Visualization of projeciton 45.

Fig. 3. Chimera visualization of mouse.tif.

Fig. 4. Slice 201 of mouse.tif using Chimera.

Fig. 5. Extraction of sinogram 201 from mouse.tif.

Fig. 6 shows the filtered back-projection of sinogram 201 extracted from moise.tif. We can see the ground truth of in Fig. 7, which is visualized using ImageJ.

Fig. 6. Extraction of sinogram 201 from mouse.tif.

Fig. 7. Extraction of sinogram 201 from mouse.tif.

Fig. 8. 3D reconstruction main loop and parameter setting.

Fig. 9. Video generation of reconstruction.

Fig. 10. Re-normalization of values to visualize reconstruction with Chimera.

Fig. 11. Visualization of results using Chimera.

J. Rico (2020) 3D reconstruction of mouse Computed Tomography using Filtered Back-projection.
[Source code](https://github.com/jvirico/mouse_CT_3D_reconstruction)

[1] - X-ray computed tomography as used in medicine. CT Scan.
[2] - Sinogram. Radon Transform.
[3] - Penczek PA. Fundamentals of three-dimensional reconstruction from projections. Methods Enzymol. 2010;482:1-33. doi:10.1016/S0076-6879(10)82001-4 .
[4] - Use of Projection and Back-projection Methods in Bidimensional Computed Tomography Image Reconstruction. Link .
[5] - Tomography and 3D imaging applied to biomedical samples. Link.