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CT reconstruction package

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CT reconstruction package


Mark Bangert (view profile)


16 Jan 2012 (Updated )

Set of functions performing ct reconstruction tasks

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Set of functions performing ct reconstruction tasks like a radon transformation, a simple backprojection, a filtered backprojection using a convolution in the spatial domain, a filtered backprojection using a 2D Fourier transformation, and a filtered back projection using the central slice theorem.

It includes the function


that should run out of the box and uses Matlab's Shepp Logan Phantom for demonstration. It is also possible to run the myCtReconstruction with an argument


to perform image reconstruction on a custom data set.


[1] Set of CT reconstruction functions by Prof. Justin Romberg @
[2] W. Schlegel, J. Bille: Medizinische Physik 2: Medizinische Strahlenphysik

MATLAB release MATLAB 7.11 (R2010b)
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Comments and Ratings (7)
17 Nov 2015 Jean-Nicola Blanchet

The function "myFilteredBackprojectionCentralSlice.m" is a simple spatial domain backprojection that does not use the slice theorem. It does the following:
- fft projections
- filter projections in Fourier domain
- ifft back to spatial
- aggregate results (spread projections and sum)

It should be done in the follwing order:
- fft projection
- filter projections in Fourier domain
- aggregate results in the Fourier domain
- ffti aggregated result back to spatial

09 Oct 2015 Saket Dandawate

The central slice algorithm[1] used in the CT package is wrong.

The central slice theorem dictated that if 1D-FT of projections is added at the center rotated at the corresponding theta then the 2D-IFT of the resultant data (in fourier domain) is equivalent to the back projections (in spacial domain).

As such visualization on the fly is only possible of the fourier domain data and not the spacial domain as you get the entire image once 2D-IFT is performed

[1] BPI = myFilteredBackprojectionCentralSlice(sinogram,thetas)

Ref :

Slide 6/7

Chapter 3 Page 56

Comment only
14 May 2015 Liz

Liz (view profile)

Can someone out here explain the reconstruction code to me?

Comment only
12 Nov 2013 Nicholas

Excellent set of code. Thanks a lot.

01 Aug 2013 Soren

Soren (view profile)

Fantastic tool for didactic purposes and as a platform for further development. Thanks for sharing!!

25 May 2012 Tai Chieh


It's really help

22 Mar 2012 Shrinivas

Excellent work

27 Jan 2012 1.2

Excluded head phantom.

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