Direct Blind Deconvolution II. Substitute Images and the BEAK Method

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 two-dimensional radially symmetric Lévy 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 f̂e(ξ, η) of the unknown exact image fe(x, y), namely, the gross behavior of log |f̂e(ξ, η)| along a single line through the origin in the (ξ, η) plane. The present paper significantly extends the applicability of the BEAK method. It is shown 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 × 512 images in the presence of noise, and includes a detailed discussion of an example where the BEAK method fails.