6 December 1996 Null space regularization and MAP reconstruction in the ill-posed inverse imaging problem
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Abstract
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 we 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 contribution using prior knowledge in a maximum-aposteriori- probability framework. We illustrate our concept by an example of optical tomographic reconstruction from simulated and experimental data.
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Ivo W. Kwee, Ivo W. Kwee, Yukari Tanikawa, Yukari Tanikawa, Sergei G. Proskurin, Sergei G. Proskurin, Simon Robert Arridge, Simon Robert Arridge, David T. Delpy, David T. Delpy, Yukio Yamada, Yukio Yamada, } "Null space regularization and MAP reconstruction in the ill-posed inverse imaging problem", Proc. SPIE 2925, Photon Propagation in Tissues II, (6 December 1996); doi: 10.1117/12.260855; https://doi.org/10.1117/12.260855
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