Model-based 2.5-d deconvolution for extended depth of field in brightfield microscopy

Due to the limited depth of field of brightfield microscopes, it is usually impossible to image thick specimens entirely in focus. By optically sectioning the specimen, the in-focus information at the specimen's surface can be acquired over a range of images. Commonly based on a high-pass criterion, extended-depth-of-field methods aim at combining the in-focus information from these images into a single image of the texture on the specimen's surface. The topography provided by such methods is usually limited to a map of selected in-focus pixel positions and is inherently discretized along the axial direction, which limits its use for quantitative evaluation. In this paper, we propose a method that jointly estimates the texture and topography of a specimen from a series of brightfield optical sections; it is based on an image formation model that is described by the convolution of a thick specimen model with the microscope's point spread function. The problem is stated as a least-squares minimization where the texture and topography are updated alternately. This method also acts as a deconvolution when the in-focus PSF has a blurring effect, or when the true in-focus position falls in between two optical sections. Comparisons to state-of-the-art algorithms and experimental results demonstrate the potential of the proposed approach.