Tomography

As an illustration of some techniques from my series of articles on tomography, I have added a tool that demonstrates basic scanning and reconstruction. Go to the tool. There are several… read more

This is the second of a two-part article on the PDART algorithm. It explains most of the nitty-gritty details. The PDART algorithm needs two extra input parameters to do its magic, a threshold and a gray level. After each SIRT iteration, each pixel of… read more

This article is a bit of an experiment. In it, I’ll try to explain PDART, an example of current algorithm research in computed tomography (PDART was published in 2011). What the algorithm does is, in a nutshell, a SIRT reconstruction with intermediate… read more

As a practical example of an iterative reconstruction algorithm, as introduced in “Tomography, Part 4: Algebra!”, I present the SIRT (Simultaneous Iterative Reconstruction Technique) algorithm. As in the mentioned article, I start from the system of linear equations… read more

Here’s a challenge for you: Reconstruct the given sinogram using the the ASTRA Tomography Toolbox that I introduced in the previous article. You’ll have to figure out the exact meaning of a sinogram like this to be able to do that. For more information… read more

If you are into computed tomography (CT) from the perspective of algorithm development, or if you want to do the reconstruction yourself instead of using a standard software package (e.g., the one that was included with your scanner), you cannot ignore the ASTRA Tomography Toolbox. This toolbox was developed by… read more

Happy Valentine’s Day! I might not be very romantic, but I had to do something with it. Imaging the heart is an important application of tomography and other techniques in medical imaging. Since hearts are everywhere on Valentine’s Day, let’s scan one. This article builds on… read more

The first three articles on tomography focused on analytic techniques, in which the reconstruction problem is attacked using mathematical analysis. When the step to real world scanners is made, the problem is discretized. Both the projections and the reconstruction area are divided into pixels, and a numerical approximation of the true mathematical technique is introduced. The algebraic techniques assume… read more

At the end of the second article on tomography, I left you with a very blurry reconstruction of the scanned object. Indeed, naive backprojection is not sufficient to create high-quality reconstructions. Why is that so? Intuitively, a simple backprojection cannot be expected to create a perfect reconstruction, since the contribution of… read more

This article shows that it is possible to reconstruct the inside of a person or object from (lots of) projections of that person or object. Mathematically, tomography is based on the fact that the function values of a two-dimension functional \(f(x,y)\) can be calculated from projections of that function. This basic fact was discovered… read more