Parameter-free Gaussian PSF Model for Extended Depth of Field in Brightfield Microscopy

Due to their limited depth of field, conventional brightfield microscopes cannot image thick specimens entirely in focus. A common way to obtain an all-in-focus image is to acquire a z-stack of images by optically sectioning the specimen and then apply a multi-focus fusion method. Unfortunately, for undersampled image stacks, fusion methods cannot remove the blur in regions where the in-focus position is between two optical sections. In this work, we propose a parameter-free Gaussian PSF model in which the all-in-focus image together with both the depth map and sampling distances in image plane are estimated from the image sequence automatically, without knowledge on the z-stack acquisition. In a maximum a posteriori framework, an iteratively reweighted least squares method is used to estimate the image and an adaptive scaled gradient descent method is utilized to estimate the depth map and sampling distances efficiently. Experiments on synthetic and real data demonstrate that the proposed method outperforms the current state-of-the-art, mitigating fusion artifacts and recovering sharper edges.