In this paper, we present an iterative reconstruction algorithm for discrete tomography, 4 called DART (Discrete Algebraic Reconstruction Technique). DART can be applied if the scanned 5 object is known to consist of only a few different compositions, each corresponding to a constant 6 grey value in the reconstruction. Prior knowledge of the grey values for each of the compositions is 7 exploit...

I comment on a paper describing a method for deducing the hidden topology of an object portrayed in a 2D natural line drawing. The principal problem with this paper is that it cannot be considered an advance on (or even an equal of) the state of the art as the approach it describes makes the same limiting assumptions as approaches proposed 10 years ago. There are also important omissions in the...

The Computed Tomography (CT) is one main imaging technique in the field of non-destructive testing. Newly, industrial robots are used to manipulate the object during the whole CT scan, instead of just placing the object onto a standard turntable as it was usual for industrial CT the times before. Using industrial robots for the object manipulation in CT systems provides an increase in spatial f...

Cryo-electron microscopy (cryo-EM) is a microscopy technique used to discover the 3D structure of molecules from very noisy 2D images. This thesis presents two projects that use algebra to describe cryo-EM datasets. In the first part, we obtain an algebraic description of common lines datasets. Common lines are lines of intersection between cryo-EM images in 3D. They are an important ingredient...

In this work we solve inverse problems coming from the area of Computed Tomography by means of regularization methods based on conjugate gradient iterations. We develop a stopping criterion which is eecient for the computation of a regularized solution for the least{squares normal equations. The stopping rule can be suitably applied also to the Tikhonov regularization method. We report computat...

In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the corresponding inference problem amenable to Expectation Maximization (EM). We present an explicit, algebraic EM-update rule for the models, yielding two fast an...