ITLApplied  Computational Mathematics Division
MCSD Highlights
Attractive Image NIST

New Efficient Approach to Blind Deconvolution of Images Discovered

March 2000

Blurred image of pyramids (left) and reconstructed image (right)
Blurred image of pyramids (left) and reconstructed image (right).

A mathematician in ITL's Mathematical and Computational Sciences Division has developed a powerful new technique for blind deconvolution of images. Blind deconvolution seeks to deblur an image without knowing the cause of the blur. This is of considerable interest in numerous medical, industrial, scientific, and military applications. The mathematical problem is very difficult and not fully understood. So far, most approaches to blind deconvolution have been iterative in nature. However, the iterative approach is generally ill-behaved, often developing stagnation points or diverging altogether. When the iterative process is stable, a large number of iterations, and several hours of computation, may be necessary to resolve fine detail.

In a recently completed research paper, Alfred Carasso has developed a novel approach to that problem that is non-iterative in nature. The method does not attempt to solve the blind deconvolution problem in full generality. Instead, attention is focused on a wide class of blurs that includes and generalizes Gaussian and Lorentzian distributions, and has significant applications. This is the class G. Likewise, a large class of sharp images is exhibited and characterized in terms of its behavior in the Fourier domain. This is the class W. It is shown how 1-D Fourier analysis of blurred image data can be used to detect class G point spread functions acting on class W images. This approach is based on empirical observations about the class W that have not previously been exploited in the literature. A separate image deblurring technique uses this detected point spread function to deblur the image. Each of these steps uses direct (non-iterative) methods. Although the new technique does require interactive adjustment of parameters, it still enables blind deblurring of 512x512 images in only minutes of CPU time on current desktop workstations.

Analysis of the blind deconvolution problem within the class G has already produced a number of interesting and unexpected results. Current research seeks to extend this approach to a wider class of blurs, in particular, out of focus blurs.

This work has already garnered considerable interest in the research community. Invited talks on this work have been or shortly will be presented at UCLA, Stanford, NIST, the Institute for Defense Analyses, the Johns Hopkins Medical School, the University of Maryland, and the Courant Institute of Mathematical Sciences of New York University. Further talks are planned at NIST-Boulder and other US Government Laboratories.

Blurred image of Uranus (left) and reconstructed image (right)
Blurred image of Uranus (left) and reconstructed image (right).

(bullet) Alfred S. Carasso (NIST/MCSD/MMG)

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