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Everything about Projection-slice theorem
Theorem in mathematics
In mathematics, the projection-slice theorem, central slice theorem or Fourier slice theorem in two dimensions states that the results of the following two calculations are equal:Take a two-dimensional function f(r), project it onto a (one-dimensional) line, and do a Fourier transform of that projection. Take that same function, but do a two-dimensional Fourier transform first, and then slice the function through its origin, parallel to the projection line. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Projection-slice theoremA 5-minute orientation
- Skim a recent paper: Extracting spectral diffusion in two-dimensional coherent spectra via the projection slice theoremInfluential work since 2022
- Pick up a classic book: Medical image analysisThe most-reprinted book on the subject
- Read the landmark paper: Characterization of resolution and uniqueness in crosswell direct-arrival traveltime tomography using the Fourier projection slice theoremCited 34 times
- Go sideways: Abel transformA closely related topic
- Go sideways: Radon transformA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Characterization of resolution and uniqueness in crosswell direct-arrival traveltime tomography using the Fourier projection slice theorem
Multidimensional Sparse Fourier Transform Based on the Fourier Projection-Slice Theorem
A Backprojection Slice Theorem for Tomographic Reconstruction
Robust initialization of 2D-3D image registration using the projection-slice theorem and phase correlation
A novel extension of the parallel‐beam projection‐slice theorem to divergent fan‐beam and cone‐beam projections
Projection-slice theorem: a compact notation
Generalized Projection-Slice Theorem for Fan Beam Diffraction Tomography
Generalized projection-slice theorem for fan beam diffraction tomography
🆕 Influential since 2022
📚 Books worth reading
Medical image analysisAtam P. Dhawan · 2010
Fourier Analysis and ImagingRonald Bracewell · 2003
Introductory medical imagingA. A. Bharath · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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