A new article is available in IPOL: http://www.ipol.im/pub/art/2018/211/
Jérémy Anger, Gabriele Facciolo, and Mauricio Delbracio,
Estimating an Image's Blur Kernel Using Natural Image Statistics, and
Deblurring it: An Analysis of the Goldstein-Fattal Method,
Image Processing On Line, 8 (2018), pp. 282–304.
https://doi.org/10.5201/ipol.2018.211
Abstract
Despite the significant improvement in image quality resulting from
improvement in optical sensors and general electronics, camera shake
blur significantly undermines the quality of hand-held photographs. In
this work, we present a detailed description and implementation of the
blur kernel estimation algorithm introduced by Goldstein and Fattal in
2012. Unlike most methods that attempt to solve an inverse problem
through a variational formulation (e.g. through a Maximum A Posteriori
estimation), this method directly estimates the blur kernel by modeling
statistical irregularities in the power spectrum of blurred natural
images. The adopted mathematical model extends the well-known power-law
by contemplating the presence of dominant strong edges in particular
directions. The blur kernel is retrieved from an estimation of its power
spectrum, by solving a phase retrieval problem using additional
constraints associated with the particular nature of camera shake blur
kernels (e.g. non-negativity and small spatial support). Although the
algorithm is conceptually simple, its numerical implementation presents
several challenges. This work contributes to a detailed anatomy of the
Goldstein and Fattal method, its algorithmic description, and its
parameters.
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