## Accurate and Fast Discrete Polar Fourier Transform (2003)

Venue: | in Proc. 37th Asilomar Conf. Signals, Systems & Computers |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Averbuch03accurateand,

author = {A. Averbuch and R. R. Coifman and D.L. Donoho and M. Elad and M. Israeli},

title = {Accurate and Fast Discrete Polar Fourier Transform},

booktitle = {in Proc. 37th Asilomar Conf. Signals, Systems & Computers},

year = {2003},

pages = {1933--1937}

}

### OpenURL

### Abstract

In this article we develop a fast high accuracy Polar FFT. For a given two-dimensional signal of size N N , the proposed algorithm's complexity is O(N log N), just like in a Cartesian 2D-FFT. A special feature of our approach is that it involves only 1-D equispaced FFT's and 1D interpolations. A central tool in our approach is the pseudo-polar FFT, an FFT where the evaluation frequencies lie in an oversampled set of non-angularly equispaced points. The pseudo-polar FFT plays the role of a halfway point -- a nearly-polar system from which conversion to Polar Coordinates uses processes relying purely on interpolation operations. We describe the conversion process, and compare accuracy results obtained by unequallysampled FFT methods to ours and show marked advantage to our approach.

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Citation Context ...ince the 1970-s and until recently. The pioneers in this field are Mersereau and Oppenheim [14] who proposed the Linogram grid as an alternative grid to the polar one. Later work by Munson and others =-=[15, 16] -=-have shown ξ xshow these ideas can be extended and used for tomography. Recently, The pseudo-polar grid (essentially the Linogram with a proper choice of oversampling) was proposed as the base for a ... |

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Accurate and Fast Discerete Polar Fourier Transform
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Citation Context ...algorithms, and discuss its features such as accuracy and computational complexity. In this paper we concentrate on the forward transform. We refer the reader to a more detailed report of our work in =-=[3]-=-. 2 Current State of the Art For evaluating the Fourier transform of a equally spaced Cartesian grid image over non-equispaced non Cartesian set of frequencies, a body of literature we refer to as USF... |