Bayesian Approach for Automatic Joint Parameter Estimation in 3D Image Reconstruction from Multi-Focus Microscope

We present a Bayesian approach for 3D image reconstruction of an extended object imaged with multi-focus microscopy (MFM). MFM simultaneously captures multiple sub-images of different focal planes to provide 3D information of the sample. The naive method to reconstruct the object is to stack the sub-images along the $z$-axis, but the result suffers from poor resolution in the $z$-axis. The maximum a posteriori framework provides a way to reconstruct a 3D image according to its observation model and prior knowledge. It jointly estimates the 3D image and the model parameters. Experimental results with synthetic and real experimental data show that it enables the high-quality 3D reconstruction of an extended object from MFM.