Lecture

Reconstruction Algorithm: X-ray Images

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Description

This lecture covers the backprojection reconstruction algorithm adapted to 1970's computing power, explaining the basic principle of filling each pixel with constant numbers corresponding to the Radon transform. It also discusses why simple backprojection has poor spatial resolution and how good image resolution can be maintained using filtered backprojection. Additionally, it explores the link between backprojection and Fourier transform through the Central Slice Theorem. The presentation includes examples and illustrations to aid understanding.

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

This course shows how existing physical principles transcend into bio-imaging and establish an important link into life sciences, illustrating the contributions physics can make to life sciences. Practical examples will be shown to illustrate the respective imaging modality, its use, premise and limitations, and biological safety will be touched upon. During this course, you will develop a good understanding of the mechanisms leading to tissue contrast of the bio-imaging modalities covered in this course, i

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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).

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.

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.

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

Fractional Fourier transform

In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.

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