Image reconstruction for 3-D light microscopy with a regularized linear method incorporating a smoothness prior
We have shown in  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 10μm fluorescent bead, and a four-cell Volvox embryo are shown.
Proceedings of SPIE - The International Society for Optical Engineering
Preza, C., Miller, M., & Conchello, J. (1993). Image reconstruction for 3-D light microscopy with a regularized linear method incorporating a smoothness prior. Proceedings of SPIE - The International Society for Optical Engineering, 129-139. https://doi.org/10.1117/12.148627