Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Direct Blind Deconvolution II. Substitute Images and the Beak Method



Alfred S. Carasso


The BEAK method is an FFT-based direct blind deconvolution technique previously introduced by the author, and applied to a limited but significant class of blurs that can be expressed as convolutions of 2-D symmetric L vy probability density functions. This class includes and generalizes Gaussian and Lorentzian distributions, but does not include defocus blurs. The method requires a-priori information on the Fourier transform e(?,?) of the unknown exact image e(x,y), namely, the gross behavior of log | e (?,?)| along asingle line through the origin in the (?,?) plane. The present paper significantly extends the applicability of the BEAK method. It isshown that images of similar objects often display approximately equal gross behavior, and that gross behavior in such substitute images can be used successfully in numerous practical contexts. Next, using substitute images, a variant of the BEAK method is developed that can handle defocus blurs. The paper is illustrated with several examples of blind deconvolution of 512 x 512 images in the presence of noise, and includes a detailed discussion of an example where the BEAK method fails.
NIST Interagency/Internal Report (NISTIR) - 6570
Report Number


BEAK method, blind deconvolution, defocusing, direct method, image deblurring, Levy density, SECB method, substitute images


Carasso, A. (2000), Direct Blind Deconvolution II. Substitute Images and the Beak Method, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed April 20, 2024)
Created November 1, 2000, Updated November 10, 2018