### Abstract

A numerically stable algorithm based on the orthogonal function solution of the 2-D Radon transform is given. This form of image reconstruction is often called circular harmonic transform (CHT) reconstruction. Series of Zernike polynomials are evaluated by solving a system of nonhomogeneous difference equations. The solution is based on a recursion formula for Zernike polynomials. We show that the method is numerically stable for the paraxial case. This algorithm overcomes the loss of spatial and constrast resolution associated with CHT algorithms. When compared with ramp-filtered back-projection, it is more resistant to ringing and it is not subject to systematic errors that seem to be caused by the discretization of the back-projection operator. The execution time is proportional to 9 N**3/32 for N**2 points on a polar grid, so that it is comparable to back-projection methods in execution time.

Original language | English (US) |
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Pages (from-to) | 873-890 |

Number of pages | 18 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 23 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1986 |

Externally published | Yes |

### ASJC Scopus subject areas

- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

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## Cite this

*SIAM Journal on Numerical Analysis*,

*23*(4), 873-890. https://doi.org/10.1137/0723056