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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position with respect to time...
Graphs of Polar Equations01:17

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
Polar Equations of Conics01:29

Polar Equations of Conics

A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can describe any conic...

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High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid.

J Cabello1, J E Gillam, M Rafecas

  • 1Instituto de Física Corpuscular, Universitat de València/CSIC, Edificio Institutos de Investigación, 22085 Valencia, Spain.

International Journal of Biomedical Imaging
|May 2, 2012
PubMed
Summary

Accelerating emission tomography image reconstruction using spherical basis functions on Graphics Processing Units (GPUs) significantly reduces computation time compared to Central Processing Units (CPUs). This GPU implementation enhances efficiency without compromising image quality.

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Area of Science:

  • Medical Imaging
  • Computational Science
  • Nuclear Medicine

Background:

  • Statistical iterative methods are standard for emission tomography image reconstruction.
  • Traditional cubic voxel models require post-reconstruction filtering, degrading spatial resolution.
  • Spherical basis functions offer lower noise but increase computational demands and system response matrix (SRM) size.

Purpose of the Study:

  • To implement and evaluate a Graphics Processing Unit (GPU) accelerated image reconstruction algorithm using spherical basis functions.
  • To improve the speed of emission tomography image reconstruction while maintaining accuracy.
  • To address the computational challenges associated with overlapping spherical basis functions.

Main Methods:

  • Implemented image reconstruction using spherical basis functions on GPU technology.
  • Utilized a precomputed Monte Carlo-calculated system response matrix (SRM) for accuracy.
  • Employed random line of response ordering and constrained atomic writing to minimize overwriting hazards.

Main Results:

  • Achieved a 4.3 times faster reconstruction time on GPU compared to Central Processing Unit (CPU).
  • Demonstrated a 2.5 times speed improvement over an eight-core CPU multi-core implementation.
  • Observed minimal differences in image quality between GPU and CPU implementations.

Conclusions:

  • GPU acceleration significantly enhances the speed of emission tomography image reconstruction with spherical basis functions.
  • The implemented method offers a viable solution to overcome the computational burden of overlapping basis functions.
  • This approach provides an efficient and accurate alternative for medical image reconstruction.