## Abstract

In statistical image reconstruction, data are often recorded on a regular grid of squares, known as pixels, and the reconstructed image is defined on the same pixel grid. Thus, the reconstruction of a continuous planar image is piecewise constant on pixels, and boundaries in the image consist of horizontal and vertical edges lying between pixels. This approximation to the true boundary can result in a loss of information that may be quite noticeable for small objects, only a few pixels in size. Increasing the resolution of the sensor may not be a practical alternative. If some prior assumptions are made about the true image, however, reconstruction to a greater accuracy than that of the recording sensor's pixel grid is possible. We adopt a Bayesian approach, incorporating prior information about the true image in a stochastic model that attaches higher probability to images with shorter total edge length. In reconstructions, pixels may be of a single color or split between two colors. The model is illustrated using both real and simulated data.

Original language | English |
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Pages (from-to) | 182-201 |

Number of pages | 20 |

Journal | Journal of Computational and Graphical Statistics |

Volume | 6 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 1997 |

## Keywords

- Bayesian statistical image reconstruction
- Confocal microscopy
- Deconvolution
- Edge detection
- Gibbs sampler
- Markov chain Monte Carlo
- Metropolis algorithm
- Subpixel resolution

## ASJC Scopus subject areas

- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Statistics, Probability and Uncertainty