Jove
Visualize
Contact Us

Related Experiment Videos

Multidimensional digital image representations using generalized Kaiser-Bessel window functions.

R M Lewitt1

  • 1Department of Radiology, University of Pennsylvania, Philadelphia 19104-6021.

Journal of the Optical Society of America. A, Optics and Image Science
|October 1, 1990
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

System models for PET statistical iterative reconstruction: A review.

Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society·2016
Same author

2.5-D simultaneous multislice reconstruction by series expansion methods from Fourier-rebinned PET data.

IEEE transactions on medical imaging·2000
Same author

Performance of the Fourier rebinning algorithm for PET with large acceptance angles.

Physics in medicine and biology·1998
Same author

Three-dimensional imaging characteristics of the HEAD PENN-PET scanner.

Journal of nuclear medicine : official publication, Society of Nuclear Medicine·1997
Same author

Practical considerations for 3-D image reconstruction using spherically symmetric volume elements.

IEEE transactions on medical imaging·1996
Same author

Fourier correction for spatially variant collimator blurring in SPECT.

IEEE transactions on medical imaging·1995
Same journal

Phase retrieval with prior information.

Journal of the Optical Society of America. A, Optics and image science·2008
Same journal

Clinical microscopy of the cornea utilizing optical sectioning and a high-numerical-aperture objective.

Journal of the Optical Society of America. A, Optics and image science·1993
Same journal

Eye-tracking laser Doppler velocimeter stabilized in two dimensions: principle, design, and construction.

Journal of the Optical Society of America. A, Optics and image science·1993
Same journal

Effects of aging in retinal image quality.

Journal of the Optical Society of America. A, Optics and image science·1993
Same journal

Axial eye-length measurement by wavelength-shift interferometry.

Journal of the Optical Society of America. A, Optics and image science·1993
Same journal

Fractal analysis of steady-state-flicker visual evoked potentials: feasibility.

Journal of the Optical Society of America. A, Optics and image science·1993
See all related articles
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

This study introduces novel discrete image representations for inverse problems in medical imaging. These methods enhance image reconstruction in applications like computerized tomography using generalized basis functions.

Area of Science:

  • Medical Imaging
  • Computational Mathematics
  • Digital Signal Processing

Background:

  • Indirect imaging applications, such as computerized tomography, often involve solving integral equations, which are inherent in inverse problems.
  • Numerical solutions require discrete representations of continuous images, posing a challenge for accurate reconstruction.
  • Existing methods may lack flexibility in handling n-dimensional spaces and specific mathematical properties.

Purpose of the Study:

  • To introduce novel discrete image representations in n-dimensional space for inverse problems.
  • To generalize the Kaiser-Bessel window function for creating rotationally symmetric basis functions.
  • To derive formulas for key mathematical operations on these basis functions and discuss their application in image reconstruction.

Main Methods:

Related Experiment Videos

  • Construction of n-dimensional, rotationally symmetric basis functions by generalizing the Kaiser-Bessel window.
  • Involvement of modified Bessel functions of order m in the generalized basis functions.
  • Derivation of formulas for Fourier transform, x-ray transform, gradient, and Laplacian of the basis functions.

Main Results:

  • Development of three methods for constructing basis functions with a specified number of continuous derivatives in n-dimensional space.
  • Formulas for essential transforms and operators applicable to the new discrete image representations.
  • Demonstration of the utility of these representations in 2D and 3D image reconstruction from line-integral data.

Conclusions:

  • The proposed discrete image representations offer a flexible and powerful approach for inverse problems in indirect imaging.
  • The generalized basis functions and derived formulas facilitate improved accuracy and efficiency in image reconstruction, particularly in computerized tomography.
  • Potential applications extend to advanced 3D image display, offering new possibilities in medical visualization.