### Samenvatting

The reconstruction problem is usually formulated as a variational problem in which one searches for that image that minimizes a so called prior (image model) while insisting on certain image features to be preserved. When the prior can be described by a norm induced by some inner product on a Hilbert space the exact solution to the variational problem can be found by orthogonal projection. In previous work we considered the image as compactly supported in and we used Sobolev norms on the unbounded domain including a smoothing parameter ¿>¿0 to tune the smoothness of the reconstruction image. Due to the assumption of compact support of the original image components of the reconstruction image near the image boundary are too much penalized. Therefore we minimize Sobolev norms only on the actual image domain, yielding much better reconstructions (especially for ¿¿»¿0). As an example we apply our method to the reconstruction of singular points that are present in the scale space representation of an image.

Originele taal-2 | Engels |
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Titel | Proceedings of the First International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2007) 30 May - 2 June 2007, Ischia, Italy |

Redacteuren | F. Sgallari, A. Murli, N. Paragios |

Plaats van productie | Berlin, Germany |

Uitgeverij | Springer |

Pagina's | 55-67 |

ISBN van geprinte versie | 978-3-540-72822-1 |

DOI's | |

Status | Gepubliceerd - 2007 |

Evenement | conference; SSVM 2007, Ischia, Italy; 2007-05-30; 2007-06-02 - Duur: 30 mei 2007 → 2 jun 2007 |

### Publicatie series

Naam | Lecture Notes in Computer Science |
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Volume | 4485 |

ISSN van geprinte versie | 0302-9743 |

### Congres

Congres | conference; SSVM 2007, Ischia, Italy; 2007-05-30; 2007-06-02 |
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Periode | 30/05/07 → 2/06/07 |

Ander | SSVM 2007, Ischia, Italy |

## Vingerafdruk Duik in de onderzoeksthema's van 'Linear image reconstruction by Sobolev norms on the bounded domain'. Samen vormen ze een unieke vingerafdruk.

## Citeer dit

Janssen, B. J., Duits, R., & Haar Romenij, ter, B. M. (2007). Linear image reconstruction by Sobolev norms on the bounded domain. In F. Sgallari, A. Murli, & N. Paragios (editors),

*Proceedings of the First International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2007) 30 May - 2 June 2007, Ischia, Italy*(blz. 55-67). (Lecture Notes in Computer Science; Vol. 4485). Springer. https://doi.org/10.1007/978-3-540-72823-8_6