Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Image Processing II: Reconstruction from Projections

In course

MICRO-512: Image processing II

Study of advanced image processing; mathematical imaging. Development of image-processing software and prototyping in Jupyter Notebooks; application to real-world examples in industrial vision and biomedical imaging. ...

Description

This lecture covers the reconstruction of images from projections in computer tomography, including the basics of the Radon transform, sinogram, backprojection, inverse Radon transform, and filtered backprojection. It also explores absorption laws, measurement principles, and various techniques and applications in tomography. The history of pioneers in the field, such as Godfrey N. Hounsfield and Alan M. Cormack, is discussed. The lecture delves into the principles of computer tomography, the Radon transform, and sampling considerations. It also explains the Radon transform, its mathematical representation, and the process of reconstructing images from projections.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (4)

Daniel Sage

Michael Stefan Daniel Liebling

Dimitri Nestor Alice Van De Ville

Michaël Unser

Official source

Ontological neighbourhood

Health sciences

Radiology: Topics in radiology

Related concepts (32)

Radon transform

In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes (integrating over lines is known as the X-ray transform).

Tomographic reconstruction

Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner.

CT scan

A computed tomography scan (usually abbreviated to CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists. CT scanners use a rotating X-ray tube and a row of detectors placed in a gantry to measure X-ray attenuations by different tissues inside the body.

Iterative reconstruction

Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques. For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually a better, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step.

X-ray

X-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.

Related lectures (33)

Reconstruction Algorithm: X-ray Images MOOC: Fundamentals of Biomedical Imaging: Ultrasounds, X-ray, positron emission tomography (PET) and applications

Explores backprojection reconstruction, spatial resolution challenges, filtered backprojection, and the link to Fourier transform.

Fourier Transforms in Tomography: Inversion Techniques

Covers the application of Fourier transforms in tomography, focusing on the Radon transform and its inversion techniques.

Tomography: Imaging by Sections

Covers the principles and applications of tomography in various fields, focusing on imaging by sections and different reconstruction techniques.

Tomography: Principles and Applications

Explores the principles and applications of tomography, covering X-ray computed tomography, electron tomography, and advanced techniques.

Gamma and Neutron Radiography