Single channel exact blind image deconvolution from radially symmmetric fir blur

The multichannel exact blind image deconvolution theory tells us that the exact image reconstruction is possible without a prior knowledge of point spread function (PSF) as long as we can measure at least three blur images through distinct blur channels. However, in many biological applications, there exist many technical difficulties in applying the theory since the specimen drift between snapshots, or specimen damage due to prolonged exposure, or physiological changes in live cell imaging. The main contribution of this paper is a new exact blind deconvolution theory that eliminates the need of multiple blur measurements, but still guarantees the exact reconstruction. The basic idea of such breakthrough is to exploit the radial symmetry of a certain class of PSFs. This makes the PSF estimation problem as 1-D channel identification problem with multiple excitations, which can be solved using subspace methods. Since radially symmetric PSFs can be quite often encountered in many practical applications such as optical imaging systems, and astigmatism corrected electron microscopy, our the theory may have great impacts in many practical imaging applications