29 July 1993 Image reconstruction for 3D light microscopy with a regularized linear method incorporating a smoothness prior
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Abstract
We have shown that the linear least-squares (LLS) estimate of the intensities of a 3-D object obtained from a set of optical sections is unstable due to the inversion of small and zero-valued eigenvalues of the point-spread function (PSF) operator. The LLS solution was regularized by constraining it to lie in a subspace spanned by the eigenvectors corresponding to a selected number of the largest eigenvalues. In this paper we extend the regularized LLS solution to a maximum a posteriori (MAP) solution induced by a prior formed from a 'Good's like' smoothness penalty. This approach also yields a regularized linear estimator which reduces noise as well as edge artifacts in the reconstruction. The advantage of the linear MAP (LMAP) estimate over the current regularized LLS (RLLS) is its ability to regularize the inverse problem by smoothly penalizing components in the image associated with small eigenvalues. Computer simulations were performed using a theoretical PSF and a simple phantom to compare the two regularization techniques. It is shown that the reconstructions using the smoothness prior, give superior variance and bias results compared to the RLLS reconstructions. Encouraging reconstructions obtained with the LMAP method from real microscopical images of a 10 micrometers fluorescent bead, and a four-cell Volvox embryo are shown.
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Chrysanthe Preza, Chrysanthe Preza, Michael I. Miller, Michael I. Miller, Jose-Angel Conchello, Jose-Angel Conchello, } "Image reconstruction for 3D light microscopy with a regularized linear method incorporating a smoothness prior", Proc. SPIE 1905, Biomedical Image Processing and Biomedical Visualization, (29 July 1993); doi: 10.1117/12.148627; https://doi.org/10.1117/12.148627
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