Single channel exact 3-D blind image deconvolution from cylindrically symmetric blur kernel

The rotational symmetry of point spread function (PSF) is common for many imaging systems such as optical microscopes, cameras, astigmatism corrected electron microscopes, and etc. In 2-D deconvolution problem, we showed that an exact PSF estimation from a single measured image on a flat background is possible by exploiting the circular symmetry. This paper extends the idea to 3-D blind deconvolution problem. More specifically, we show that the exact recovery of 3-D PSF is possible from a single set of z-stack images if the PSF of the microscope has a cylindrical symmetry and there exists enough working distance to cover the volumetric sample from top to bottom. The resulting algorithm allows an accurate computational optical sectioning of biological specimen from z-stack images using brightfield or fluorescence microscopes without separate PSF measurements. Experimental results confirm our theory.