## B. Non-Uniform Fast Fourier Transform C. Fourier-Based Iterative Reconstruction D. Emulation of Image Representation Using Basis Functions (2003)

### BibTeX

@MISC{Matej03b.non-uniform,

author = {Samuel Matej and Jeffrey A. Fessler and Ivan G. Kazantsev},

title = {B. Non-Uniform Fast Fourier Transform C. Fourier-Based Iterative Reconstruction D. Emulation of Image Representation Using Basis Functions},

year = {2003}

}

### OpenURL

### Abstract

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Citation Context ... �¥��������� ��� � � � ���¥��������� ��� ��� ��� ����� � � ����� ��������� � ��� (9) for and value zero for , where is the distance from the KB kernel center, � denotes the modified � Bessel function =-=[32]-=- of order � , � is the size of the KB window and � is a parameter controlling the KB window shape and frequency characteristics [29, 30] (see examples of KB window functions and of their spectra in Fi... |

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Citation Context ...as , where . Let denote the - dimensional image whose projections (the ray transform) we wish to compute. Let be the image spectrum, obtained by Fourier transform (2) Then the central section theorem =-=[11]-=- is given by (3) where � ������� � ������� ��������� � � ������� � � ��� � ����� � � � � � ��� � � ����� ��������� � ����� � ��� ������� � ��������� ��� � � ����� � (4) � image spectrum , , distribute... |

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Citation Context ...e crucial step influencing the reconstruction quality and speed is the interpolation between polar and Cartesian rasters in frequency space. Gridding interpolation [18, 19], with proper interpolating =-=[20]-=- and data weighting functions, as investigated in the MRI literature [21–23], brought improvement in the direct Fourier reconstruction. Recently, the Fourier-based reprojection has been applied for (n... |

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Citation Context ...nsform (NUFFT) [26] used in this paper is related to gridding methods for interpolation in frequency space. The KB interpolation kernels used in this work have been optimized using a min-max approach =-=[27]-=-, thus providing substantial improvement of the interpolation accuracy. In the previous works on gridding, the focus was on using the interpolation to find a non-iterative approximate solution to an i... |

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Citation Context ...ction operation (e.g., [16, 17]). The crucial step influencing the reconstruction quality and speed is the interpolation between polar and Cartesian rasters in frequency space. Gridding interpolation =-=[18, 19]-=-, with proper interpolating [20] and data weighting functions, as investigated in the MRI literature [21–23], brought improvement in the direct Fourier reconstruction. Recently, the Fourier-based repr... |

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Citation Context ...essel (KB) windows were used for interpolation, which are known to be reasonably accurate but without explicitly evaluating the accuracy. The concept of the non-uniform Fast Fourier transform (NUFFT) =-=[26]-=- used in this paper is related to gridding methods for interpolation in frequency space. The KB interpolation kernels used in this work have been optimized using a min-max approach [27], thus providin... |

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