Discrete tomography deals with tomographic reconstruction of greyscale images for which the set of possible grey levels is discrete and small. Here, we develop a discrete approximate reconstruction algorithm. Our algorithm computes an image that has only grey values belonging to a given finite set. It also guarantees that the difference between the given projections and the projections of the r...

The problem of reconstructing finite subsets of the integer lattice from X-rays has been studied in discrete mathematics and applied in several fields like image processing, data security, electron microscopy. In this paper we focus on the stability of the reconstruction problem for some lattice sets. First we show some theoretical bounds for additive sets, and a numerical experiment is made by...

In tomography, slight differences between the geometry of the scanner hardware and the geometric model used in the reconstruction lead to alignment artifacts. To exploit high-resolution detectors used in many applications of tomography, alignment of the projection data is essential. Markerless alignment algorithms are the preferred choice over alignment with markers, in case a fully automatic t...

objectives to evaluate morphologic variations at the aortic isthmus with particular attention to ductus diverticulum, a mimicker of traumatic pseudoaneurysm, and to describe differences using computed tomography (ct) images. patients and methods from december 2013 to december 2014, patients who underwent a chest ct examination after blunt trauma at our emergency department were included. aortic...

planar d-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as electrical impedance tomography (eit). recently two different methodologies are considered for the numerical solution of d-bar integrals equation, namely product integrals and multigrid. the first one involves high computational ...

As the Computed Tomography (CT) requires normally hundreds of projections to reconstruct the image, patients are exposed to more X-ray energy, which may cause side effects such as cancer. Even when the variability of the particles in the object is very less, the Computed Tomography requires many projections for good quality reconstruction. Discrete Tomography makes use of less variability of th...

We present a 3D zigzag rafter -first in literaturewhich allows us to obtain the exact sequence of spectral components after application of Discrete Cosine Transform 3D (DCT-2D) over a cube. Such cube represents part of a video or eventually a group of images such as multi-slicing (e.g., Magnetic Resonance or Computed Tomography imaging) and multi or hyperspectral imagery (optical satellites). B...

Path Puzzles are a type of logic puzzle introduced in Roderick Kimball’s 2013 book [5]. A puzzle consists of a (rectangular) grid of cells with two exits (or “doors”) on the boundary and numerical constraints on some subset of the rows and columns. A solution consists of a single non-intersecting path which starts and ends at two boundary doors and which passes through a number of cells in each...