Single channel blind image deconvolution from radially symmetric blur kernels

The multichannel exact blind image deconvolution theory tells us that exact recovery of unknown blur kernels is possible from multiple measurements of an identical scene through distinct blur channels. However, in many biological applications, there often exist technical difficulties in obtaining multiple distinct blur measurements, since the image content may vary for various reasons, including specimen drift between snapshots, specimen damage due to prolonged exposure, or physiological changes in live cell imaging. The main contribution of this paper is a new non-iterative single channel blind deconvolution method that eliminates the need of multiple blur measurements, but still guarantees an accurate estimation of the blurring kernel. The basic idea behind this novel method is to exploit the radial symmetry of a certain class of PSFs. This approach simplifies the PSF estimation to a 1-D channel identification problem with multiple excitations, which can be solved using a standard subspace method. Since radially symmetric PSFs are quite often encountered in many practical applications, such as optical imaging systems and electron microscopy, our theory may have great influence on many practical imaging applications. Simulation results as well as real experimental results using optical and electron microscopy confirm our theory.