### Abstract

We present a solution method for adaptively smoothing magnetic resonance (MR) images while preserving discontinuities. We assume that the spatial behavior of MR data can be captured by a first order polynomial defined at every pixel. The formulation itself is similar to Leclerc's work on piecewise-smooth image segmentation, but we use the graduated non- convexity (GNC) algorithm as an optimizing tool for obtaining the solution. This requires initial values for polynomial coefficients of order greater than zero. These values are obtained by using ideas similar to that found in robust statistics. This initial step is also useful in determining the variance of the noise present in the input image. The variance is related to an important parameter α required by the GNC algorithm. Firstly, this replaces the heuristic nature of α with a quantity that can be estimated. Secondly, it is useful especially in situations where the variance of the noise is not uniform across the image. We present results on synthetic and MR images. Though the results of this paper are given using first order polynomials, the formulation can handle higher order polynomials.

Original language | English (US) |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Publisher | Publ by Int Soc for Optical Engineering |

Pages | 422-431 |

Number of pages | 10 |

ISBN (Print) | 0819408042 |

State | Published - Jan 1 1992 |

Event | Medical Imaging VI: Image Processing - Newport Beach, CA, USA Duration: Feb 24 1992 → Feb 27 1992 |

### Publication series

Name | Proceedings of SPIE - The International Society for Optical Engineering |
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Volume | 1652 |

ISSN (Print) | 0277-786X |

### Other

Other | Medical Imaging VI: Image Processing |
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City | Newport Beach, CA, USA |

Period | 2/24/92 → 2/27/92 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

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## Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(pp. 422-431). (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 1652). Publ by Int Soc for Optical Engineering.