Nullspace regularization and MAP reconstruction in the ill-posed inverse imaging problem.
PHOTON PROPAGATION IN TISSUES II, PROCEEDINGS OF
43 - 54.
The ill-posed inverse problem is not an issue that is only restricted to optical tomography, but indeed a very common issue in image reconstruction problems in astronomy, geological surveying, and medical imaging in general. In this paper toe investigate the consequences of ill-posed problems, and show that correct reconstruction is generally not possible using conventional linear inversion techniques because latter methods disregard contributions of the nullspace. We describe the rationale of a novel image reconstruction method that estimates the nullspace contibution using prior knowledge in a maximum-aposteriori-probability (MAP) framework. We illustrate our concept by an example of optical tomographic reconstruction from simulated and experimental data.
|Title:||Nullspace regularization and MAP reconstruction in the ill-posed inverse imaging problem|
|Keywords:||optical tomography, image reconstruction, maximum a posteriori probability, ill-posed problems, Bayesian probability, prior knowledge|
|UCL classification:||UCL > School of BEAMS
UCL > School of BEAMS > Faculty of Engineering Science
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