Estimating an Image's Blur Kernel Using Natural Image Statistics, and Deblurring it: An Analysis of the Goldstein-Fattal Method
Jérémy Anger, Gabriele Facciolo, Mauricio Delbracio
→ BibTeX
@article{ipol.2018.211,
    title   = {{Estimating an Image's Blur Kernel Using Natural Image Statistics, and Deblurring it: An Analysis of the Goldstein-Fattal Method}},
    author  = {Anger, Jérémy and Facciolo, Gabriele and Delbracio, Mauricio},
    journal = {{Image Processing On Line}},
    volume  = {8},
    pages   = {282--304},
    year    = {2018},
    doi     = {10.5201/ipol.2018.211},
}
% if your bibliography style doesn't support doi fields:
    note    = {\url{https://doi.org/10.5201/ipol.2018.211}}
published
2018-09-26
reference
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

Communicated by Julie Delon
Demo edited by Jérémy Anger

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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