### Abstract

We present a method to reconstruct images from finite sets of noisy projections that may be available only over limited or sparse angles. The algorithm calculates the maximum a posteriori (MAP) estimate of the full sinogram (which is an image of the 2-D Radon transform of the object) from the available data. It is implemented using a primal-dual constrained optimization procedure that solves a partial differential equation in the primal phase with an efficient local relaxation algorithm and uses a simple Lagrange-multiplier update in the dual phase. The sinogram prior probability is given by a Markov random field (MRF) that includes information about the mass, center of mass, and convex hull of the object, and about the smoothness, fundamental constraints, and periodicity of the 2-D Radon transform. The object is reconstructed using convolution backprojection applied to the estimated sinogram. We show several reconstructed objects which are obtained from simulated limited- and sparse-angle data using the described algorithm, and compare these results with images obtained using convolution backprojection directly.

Original language | English (US) |
---|---|

Pages (from-to) | 151-191 |

Number of pages | 41 |

Journal | Linear Algebra and Its Applications |

Volume | 130 |

Issue number | C |

DOIs | |

State | Published - Mar 1990 |

Externally published | Yes |

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'A geometric projection-space reconstruction algorithm'. Together they form a unique fingerprint.

## Cite this

*Linear Algebra and Its Applications*,

*130*(C), 151-191. https://doi.org/10.1016/0024-3795(90)90211-T