A problem of blind deconvolution arises when one attempts to restore a short-exposure image that has been degraded by random atmospheric turbulence. We attack the problem by using two short-exposure images as data inputs. The Fourier transform of each is taken, and the two are divided. The result is the quotient of the two unknown transfer functions. The latter are expressed, by means of the sampling theorem, as Fourier series in corresponding point-spread functions, the unknowns of the problem. Cross multiplying the division equation gives an equation that is linear in the unknowns. However, the problem has, initially, a multiplicity of solutions. This deficiency is overcome by use of the prior knowledge that the object and the point-spread functions have finite (albeit unknown) support extensions and also are positive. The result is a fixed-length, linear algorithm that is regularized to the presence of 4–15% additive noise of detection.
© 1999 Optical Society of America
Original Manuscript: July 2, 1998
Revised Manuscript: November 19, 1998
Published: April 10, 1999
Sergio Barraza-Felix and B. Roy Frieden, "Regularization of the image division approach to blind deconvolution," Appl. Opt. 38, 2232-2239 (1999)