Journal ArticleDOI
Hexagonal fast Fourier transform with rectangular output
TLDR
A separable fast discrete Fourier transform (DFT) algorithm for hexagonally sampled data that directly computes output points on a rectangular lattice is reported.Abstract:
Hexagonal sampling is the most efficient sampling pattern for a two-dimensional circularly bandlimited function. A separable fast discrete Fourier transform (DFT) algorithm for hexagonally sampled data that directly computes output points on a rectangular lattice is reported. No interpolation is required. The algorithm has computational complexity comparable to that of standard two-dimensional fast Fourier transforms. >read more
Citations
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Journal ArticleDOI
Ultra-fast MRI of the human brain with simultaneous multi-slice imaging.
TL;DR: This parallel imaging technique began over a decade ago and through recent sequence improvements has reduced the acquisition time of multi-slice EPI by over ten fold.
Journal ArticleDOI
Fingerprint classification using a hexagonal fast fourier transform
A.P. Fitz,R.J. Green +1 more
TL;DR: A Hexagonal Fourier Transform is applied that will classify fingerprints into whorls, loops and arches, which allows the utilization of hexagonally sampled data and the extention of output data in a rectangular scheme, which is more convenient for treatment and interpretation.
Journal ArticleDOI
Hex-splines: a novel spline family for hexagonal lattices
TL;DR: A new family of bivariate, nonseparable splines, called hex-splines, especially designed for hexagonal lattices, is proposed, and important properties, such as their Fourier transform and the fact they form a Riesz basis are discussed.
Proceedings ArticleDOI
Hexagonal Structure for Intelligent Vision
Xiangjian He,Wenjing Jia +1 more
TL;DR: In this article, typical hexagonal coordinates and addressing schemes, as well as hexagonal based image processing and applications are fully reviewed, and general reasons that hexagonally sampled images are chosen for research are introduced.
Journal ArticleDOI
Sub-Hexagonal Phase Correlation for Motion Estimation
TL;DR: A novel frequency-domain motion estimation technique, which operates on hexagonal images and employs the hexagonal Fourier transform, which outperforms the state-of-the-art in frequency- domain motion estimation operating on a square lattice in terms of subpixel accuracy for a range of test material and motion scenarios.
References
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Book
Two-Dimensional Signal and Image Processing
TL;DR: This text covers the principles and applications of "multidimensional" and "image" digital signal processing and is suitable for Sr/grad level courses in image processing in EE departments.
Journal ArticleDOI
Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces
TL;DR: The well-known Whittaker-Kotel'nikov-Shannon sampling theorem for frequency-bandlimited functions of time is extended to functions of multidimensional arguments and it is shown that a function whose spectrum is restricted to a finite region of wave-number space may be reconstructed from its samples taken over a periodic lattice having suitably small repetition vectors.
Journal ArticleDOI
An algorithm for computing the mixed radix fast Fourier transform
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.
Journal ArticleDOI
The processing of hexagonally sampled two-dimensional signals
TL;DR: Methods for the processing of two- dimensional signals which have been sampled as two-dimensional hexagonal arrays are presented and some comparisons between the two methods for representing planar data will also be presented.
Book
Fast Transforms Algorithms, Analyses, Applications
TL;DR: This chapter discusses Fourier Series and Fourier Transform Algorithms, Discrete Fourier Transforms, DFT Filter Shapes and Shaping, and Spectral Analysis Using the FFT.