Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis
Abstract
The problem of image reconstruction in emission tomography in an ill-posed inverse problem. The methodology FRECT (Fourier regularized computed tomography) allows not only for a priori analysis of the stability of the reconstruction process but also for an exact definition of the resolution in the slices. Its natural regularization parameter, namely the cutoff frequency ν of the filter underlying the definition of the FRECT solution, can be calibrated by estimating the condition number for a range of values of ν . We first outline the methodology FRECT. We then discuss the numerical strategies which can be implemented in order to estimate the condition numbers of large matrices. Finally, we present a few results obtained in the context of SPECT reconstructions, and discuss the possibility to determine automatically the best possible cutoff frequency from the analysis of the stability.
Cite
Text
Maréchal et al. "Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis." European Conference on Computer Vision, 2004. doi:10.1007/978-3-540-27816-0_6Markdown
[Maréchal et al. "Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis." European Conference on Computer Vision, 2004.](https://mlanthology.org/eccv/2004/marechal2004eccv-automatic/) doi:10.1007/978-3-540-27816-0_6BibTeX
@inproceedings{marechal2004eccv-automatic,
title = {{Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis}},
author = {Maréchal, P. and Mariano-Goulart, Denis and Giraud, Luc and Gratton, Serge},
booktitle = {European Conference on Computer Vision},
year = {2004},
pages = {64-74},
doi = {10.1007/978-3-540-27816-0_6},
url = {https://mlanthology.org/eccv/2004/marechal2004eccv-automatic/}
}