Title:		Investigation of Blind Deconvolution Algorithms


Students:	Rui Zhang	--	rzhang@stanford.edu
		Yirong Shen	--	yirong99@stanford.edu


Project Description:

In imaging systems, the true, desired image f(x,y) is convolved by a
blurring point spread function h(x,y), and then corrupted by an additive
random noise n(x,y), so that the resulting image is 

	g(x,y) = f(x,y) * h(x,y) + n(x,y)

Blind deconvolution is the problem of restoring from the degraded image
g(x,y) both the true image f(x,y) and the point spread function
h(x,y) while having little or no a priori information about either.

In this project, we propose to implement, test, and compare 2 or more
algorithms from literature for blind deconvolution.  If time permitting,
we will also attempt to improve the preformance of one of the algorithms. 

The first algorithm that we will study is the iterative blind
deconvolution (IBD) method as described by Ayers and Dainty.  The IBD
algorithm operates by alternately imposing image and fourier domain
constraints on the estimated image and the estimated point spread
function.  The IBD algorithm makes the assumption that both f(x,y) and
h(x,y) have finite support and take on only non-negative values.  

The second algorithm that we will study is based on projection onto
convex sets (POCS).   The POCS method considers functions that satisfy
pieces of a priori information as forming closed convex sets.  It then
successively projects the estimates for f(x,y) and h(x,y) onto these
convex sets to obtain the estimate for f(x,y).


References:

G. Ayers and J. Dainty, "Iterative blind deconvolution method and its
applications," Optics Letters, vol. 13. pp.547-549, July 1988

R. Bates and H. Jiang, "Blind deconvolution - recovering the seemingly
irrecoverable!," in International Trends in Optics (J.W. Goodman, ed.),
pp.423-437, 1991