Spatially adaptive 3D inverse for optical sectioning

In this paper, we propose a novel nonparametric approach to reconstruction of three-dimensional (3D) objects from 2D blurred and noisy observations which is a problem of computational optical sectioning. This approach is based on an approximate image formation model which takes into account depth varying nature of blur described by a matrix of shift-invariant 2D point-spread functions (PSF ) of an optical system. The proposed restoration scheme incorporates the matrix regularized inverse and matrix regularized Wiener inverse algorithms in combination with a novel spatially adaptive denoising. This technique is based on special statistical rules for selection of the adaptive size and shape neighbourhood used for the local polynomial approximation of the 2D image intensity. The simulations on a phantom 3D object show efficiency of the developed approach. The objective result evaluation is presented in terms of quadratic-error criteria.